# zbMATH — the first resource for mathematics

## Geombinatorics

### A Journal of Open Problems of Combinatorial and Discrete Geometry and Related Areas

 Short Title: Geombinatorics Publisher: University of Colorado and Center for Excellence in Mathematical Education, Colorado Springs, CO ISSN: 1065-7371 Online: http://www.uccs.edu/~geombina/
 Documents Indexed: 437 Publications (since 1991)
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#### Latest Issues

 31, No. 1 (2021) 30, No. 4 (2021) 30, No. 3 (2021) 30, No. 2 (2020) 30, No. 1 (2020) 29, No. 4 (2020) 29, No. 3 (2020) 29, No. 2 (2019) 29, No. 1 (2019) 28, No. 4 (2019) 28, No. 3 (2019) 28, No. 2 (2018) 28, No. 1 (2018) 27, No. 4 (2018) 27, No. 3 (2018) 27, No. 2 (2017) 27, No. 1 (2017) 26, No. 4 (2017) 26, No. 3 (2017) 26, No. 2 (2016) 26, No. 1 (2016) 25, No. 4 (2016) 25, No. 3 (2016) 25, No. 2 (2015) 25, No. 1 (2015) 24, No. 4 (2015) 24, No. 3 (2015) 24, No. 2 (2014) 24, No. 1 (2014) 23, No. 4 (2014) 23, No. 3 (2014) 23, No. 2 (2013) 23, No. 1 (2013) 22, No. 4 (2013) 22, No. 3 (2013) 22, No. 2 (2012) 22, No. 1 (2012) 21, No. 4 (2012) 21, No. 3 (2012) 21, No. 2 (2011) 21, No. 1 (2011) 20, No. 4 (2011) 18, No. 2 (2008) 18, No. 1 (2008) 15, No. 3 (2006) 15, No. 2 (2005) 14, No. 3 (2005) 14, No. 2 (2004) 14, No. 1 (2004) 13, No. 4 (2004) 13, No. 3 (2004) 13, No. 2 (2003) 13, No. 1 (2003) 12, No. 4 (2003) 12, No. 3 (2003) 12, No. 2 (2002) 12, No. 1 (2002) 11, No. 4 (2002) 11, No. 3 (2002) 11, No. 2 (2001) 11, No. 1 (2001) 10, No. 4 (2001) 10, No. 3 (2001) 10, No. 2 (2000) 10, No. 1 (2000) 9, No. 4 (2000) 9, No. 3 (2000) 9, No. 2 (1999) 9, No. 1 (1999) 8, No. 4 (1999) 8, No. 3 (1999) 8, No. 2 (1998) 8, No. 1 (1998) 7, No. 4 (1998) 7, No. 3 (1998) 7, No. 2 (1997) 7, No. 1 (1997) 6, No. 4 (1997) 6, No. 3 (1997) 6, No. 2 (1996) 6, No. 1 (1996) 5, No. 4 (1996) 5, No. 3 (1996) 5, No. 2 (1995) 5, No. 1 (1995) 4, No. 4 (1995) 4, No. 3 (1995) 4, No. 2 (1994) 4, No. 1 (1994) 3, No. 4 (1994) 3, No. 3 (1994) 3, No. 2 (1993) 3, No. 1 (1993) 2, No. 4 (1993) 2, No. 3 (1993) 2, No. 2 (1992) 2, No. 1 (1992) 1, No. 4 (1992) 1, No. 3 (1991) 1, No. 2 (1991)
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#### Authors

 55 Grünbaum, Branko 49 Soifer, Alexander 44 Kreinovich, Vladik Yakovlevich 19 Kosheleva, Olga M. 17 Erdős, Pál 16 Johnson, Peter D. jun. 13 Pach, János 11 Kuzminykh, Alexandr Veniaminovich 10 Harborth, Heiko 8 Friedman, Erich 8 Zaks, Joseph 7 Rosenfeld, Moshe 6 Ismailescu, Dan P. 6 Januszewski, Janusz 6 Kahle, Matthew 6 Kainen, Paul C. 6 O’Donnell, Paul 5 Parts, Jaan 5 Tóth, Géza 4 Exoo, Geoffrey 4 Khan, Samee Ullah 3 Brass, Peter 3 Brown, Nathanial P. 3 Burger, Alewyn Petrus 3 Chilakamarri, Kiran B. 3 Czyzowicz, Jurek 3 Dinkelacker, Peter 3 Dunfield, Nathan M. 3 Finkelstein, Andrei M. 3 Khovanova, Tanya 3 Koshelev, Misha 3 Lassak, Marek 3 Lerma, Octavio 3 Malen, Greg 3 Marcu, Dănuţ 3 Möller, Meinhard 3 Noble, Matthew 3 Perry, Greg 3 Praton, Iwan 3 Roldán, Érika 3 Shelah, Saharon 3 Starks, Scott A. 3 Vogel, Stefan 3 Wetzel, John E. 3 Winkler, Mike 3 Wolff von Gudenberg, Jürgen 2 Abrams, Aaron 2 Alm, Jeremy F. 2 Alonso, Orlando B. 2 Anderson, Loren 2 Bacher, Roland 2 Bokati, Laxman 2 Bose, Prosenjit K. 2 Carrigan, Braxton 2 de Grey, Aubrey D. N. J. 2 Fishburn, Peter Clingerman 2 Garber, David 2 Greenwell, Don 2 Hochberg, Robert A. 2 Hoffman, Ilya 2 Horák, Peter 2 Iourinski, Dima 2 Kranakis, Evangelos Konstantinou 2 Kurz, Sascha 2 Lángi, Zsolt 2 Lengvárszky, Zsolt 2 Malkevitch, Joseph 2 Mann, Matthias 2 Molchanov, Ilya S. 2 Nešetřil, Jaroslav 2 Rabinowitz, Stanley 2 Raedschelders, Peter 2 Shephard, Geoffrey Colin 2 Wagon, Stan 2 Wawrzycki, Jarosław 1 Ahn, Hee-Kap 1 Alarcon, Eberth G. II 1 Alfaro, Richard 1 Ambainis, Andris 1 An, Seung Hwan 1 Aroux, Denis 1 Atkinson, Bruce W. 1 Bailey-Kellogg, Chris 1 Bálint, Vojtech 1 Bálint, Vojtech jun. 1 Bankov, Kiril 1 Barry, Matthew 1 Bean, Dwight R. 1 Beck, Jan B. 1 Bennett, Katherine 1 Berglund, Kenneth 1 Bertram, Edward Arthur 1 Bikov, Aleksandar 1 Binder, Kyle 1 Blanc, Jérémy 1 Bode, Jens-P. 1 Bohannon, A. W. 1 Bohannon, Aaron 1 Bouchon-Meunier, Bernadette 1 Brewer, Majorie ...and 184 more Authors
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#### Fields

 195 Combinatorics (05-XX) 162 Convex and discrete geometry (52-XX) 85 Geometry (51-XX) 41 History and biography (01-XX) 17 Computer science (68-XX) 13 Number theory (11-XX) 13 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 9 General and overarching topics; collections (00-XX) 8 Mathematical logic and foundations (03-XX) 6 Numerical analysis (65-XX) 5 Manifolds and cell complexes (57-XX) 5 Relativity and gravitational theory (83-XX) 4 Differential geometry (53-XX) 4 Probability theory and stochastic processes (60-XX) 4 Operations research, mathematical programming (90-XX) 3 Functional analysis (46-XX) 3 General topology (54-XX) 3 Mechanics of deformable solids (74-XX) 3 Geophysics (86-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Group theory and generalizations (20-XX) 2 Measure and integration (28-XX) 2 Statistics (62-XX) 2 Astronomy and astrophysics (85-XX) 2 Mathematics education (97-XX) 1 Commutative algebra (13-XX) 1 Algebraic geometry (14-XX) 1 Real functions (26-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Algebraic topology (55-XX) 1 Mechanics of particles and systems (70-XX) 1 Optics, electromagnetic theory (78-XX) 1 Quantum theory (81-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Biology and other natural sciences (92-XX) 1 Systems theory; control (93-XX) 1 Information and communication theory, circuits (94-XX)

#### Citations contained in zbMATH Open

116 Publications have been cited 332 times in 262 Documents Cited by Year
Colorings of metric spaces. Zbl 0951.05037
Benda, M.; Perles, M.
2000
Thirteen problems on crossing numbers. Zbl 0957.05026
Pach, János; Tóth, Géza
2000
The chromatic number of the plane is at least. Zbl 1404.05063
de Grey, Aubrey D. N. J.
2018
Choosability versus chromaticity—the plane unit distance graph has a $$2$$-chromatic subgraph of infinite list-chromatic number. Zbl 0855.05055
Jensen, Tommy R.; Toft, Bjarne
1995
A Ramsey-type theorem for bipartite graphs. Zbl 0978.05052
Erdős, Paul; Hajnal, András; Pach, János
2000
Chromatic number of the plane: A historical essay. Zbl 0853.05038
Soifer, Alexander
1991
Comment on Fox news. Zbl 1145.05020
Pach, János; Tóth, Géza
2006
On the chromatic number of real and rational spaces. Zbl 1190.05067
Cibulka, Josef
2008
Chromatic number of the plane and its relatives. Zbl 1035.05043
Soifer, Alexander
2003
Midpoints of segments induced by a point set. Zbl 1060.11015
Pach, János
2003
Arbitrary girth, 4-chromatic unit distance graphs in the plane.  I: Graph description. Zbl 0937.05038
O’Donnell, Paul
2000
Arbitrary girth, 4-chromatic unit distance graphs in the plane. II: Graph embedding. Zbl 0979.05045
O’Donnell, Paul
2000
Uniform tilings of $$3$$-space. Zbl 0844.52022
Grünbaum, Branko
1994
The edge Folkman number $$F_e(3,3;4)$$ is greater than 19. Zbl 1373.05116
Bikov, Aleksandar; Nenov, Nedyalko
2017
Monochromatic intersection points in families of colored lines. Zbl 0948.52013
Grünbaum, Branko
1999
Astral $$(n_4)$$ configurations. Zbl 0981.51014
Grünbaum, Branko
2000
Astral $$(n_ k)$$ configurations. Zbl 0845.51010
Grünbaum, Branko
1993
Connected $$(n_4)$$ configurations exist for almost all $$n$$ – an update. Zbl 1116.52302
Grünbaum, Branko
2002
On four points of a convex body in large relative distances. Zbl 1061.52001
Lángi, Zsolt; Lassak, Marek
2003
On polygons enclosing point sets. Zbl 1004.52001
Czyzowicz, Jurek; Hurtado, Ferran; Urrutia, Jorge; Zaguia, Nejib
2001
The list-chromatic number of Euclidean space. Zbl 0847.05056
Schmerl, James H.
1995
On the independence number of coin graphs. Zbl 0853.05051
Pach, János; Tóth, Géza
1996
Chromatic number of the plane and its relatives. II: Polychromatic number and 6-coloring. Zbl 1061.05038
Soifer, Alexander
2003
Tiling the plane with equilateral triangles. Zbl 1430.52027
Pach, János; Tardos, Gábor
2019
The search for symmetric Venn diagrams. Zbl 0929.52007
Grünbaum, Branko
1999
A relative of “Napoleon’s theorem”. Zbl 0979.51008
Grünbaum, Branko
2001
No-net polyhedra. Zbl 1010.52010
Grünbaum, Branko
2002
Nets of polyhedra. II. Zbl 0845.51019
Grünbaum, Branko
1991
Venn diagrams. II. Zbl 0851.52009
Grünbaum, Branko
1992
Hamiltonian polygons and polyhedra. Zbl 0845.05066
Grünbaum, Branko
1994
Which algorithms are feasible and which are not depends on the geometry of space-time. Zbl 0844.68060
1995
How to convexify a polygon. Zbl 0866.52001
Grünbaum, Branko
1995
Some 4-chromatic unit-distance graphs without small cycles. Zbl 0855.05056
Hochberg, Robert; O’Donnell, Paul
1996
Covering squares with unit squares. Zbl 1097.52005
Friedman, Erich; Paterson, David A.
2006
Open-ended configurations of radio telescopes: A geometrical analysis. Zbl 1142.85300
Kreinovich, Vladik; Starks, Scott A.; Iourinski, Dima; Kosheleva, Olga; Finkelstein, Andrei
2003
Examples on the plane and $$R^n$$. Zbl 1057.03037
Soifer, Alexander; Shelah, Saharon
2004
On the number of points at distance at least 1 in the unit cube. Zbl 1061.52003
Bálint, Vojtech; Bálint, Vojtech jun.
2003
30 two-colored points with no empty monochromatic convex fourgons. Zbl 1063.52011
Friedman, Erich
2004
New lower bounds on $$\chi ({\mathbb R}^d)$$ for $$d = 8,\dots, 12$$. Zbl 1327.05247
Kahle, Matthew; Taha, Birra
2015
Coloring distance graphs: a few answers and many questions. Zbl 1334.05039
Kloeckner, Benoît R.
2015
Computing small unit-distance graphs with chromatic number 5. Zbl 1404.05054
Heule, Marijn J. H.
2018
More on the fractional chromatic number. Zbl 0941.05024
Johnson, P. D. jun.
1999
Ahn, Hee-Kap; Bose, Prosenjit; Czyzowicz, Jurek; Hanusse, Nicolas; Kranakis, Evangelos; Morin, Pat
2000
Forbidding prescribed distances for designated colors. Zbl 0848.05030
Greenwell, Don; Johnson, Peter D. jun.
1992
Triangles in convex polygons. Zbl 0844.52002
Erdős, Paul; Soifer, Alexander
1993
Is Snaky a winner? Zbl 0847.05039
Harary, Frank
1993
$$O(n^ 3)$$ bounds for the area of a convex lattice $$n$$-gon. Zbl 0847.52013
Rabinowitz, Stanley
1993
Quadrangles, pentagons, and computers. Zbl 0845.51013
Grünbaum, Branko
1993
The choice number of the plane. Zbl 0848.05031
Johnson, Peter D. jun.
1994
Squares in a square. Zbl 0850.52013
Erdős, Paul; Soifer, Alexander
1995
Odd integral distances among points in the plane. Zbl 0844.52010
Rosenfeld, Moshe
1996
Folding and turning along geodesics in a convex surface. Zbl 0892.52004
Pach, János
1997
Ordered black boxes: existence. Zbl 1314.03042
Shelah, Saharon
2014
A note on convex realizability of arrangements of pseudocircles. Zbl 1159.52022
Linhart, Johann; Ortner, Ronald
2008
Tromino tiling deficient cubes of side length $$2^n$$. Zbl 1184.05020
Starr, Norton
2008
Note on covering square with equal squares. Zbl 1162.52011
Karabash, Dmytro; Soifer, Alexander
2008
The best polynomial bounds for the number of triangles in a simple arrangement of $$n$$ pseudo-lines. Zbl 1335.52032
Blanc, Jérémy
2011
Polyiamonds attaining extremal topological properties. I. Zbl 1458.52012
Malen, Greg; Roldán, Érika
2020
Graph minimization, focusing on the example of 5-chromatic unit-distance graphs in the plane. Zbl 1452.05070
Parts, Jaan
2020
A unit distance graph in the plane with fractional chromatic number 383/102. Zbl 1360.05032
Exoo, Geoffrey; Ismailescu, Dan
2017
Polyominoes with maximally many holes. Zbl 1428.05052
Kahle, Matthew; Roldán, Érika
2019
Squares touching a constant number of other squares. Zbl 1041.52009
Friedman, Erich
2002
(1-2-3)-complexes. Zbl 1045.52004
Grünbaum, Branko
2003
Hunting unit-distance graphs in rational $$n$$-spaces. Zbl 1054.05041
Mann, Matthias
2003
Are prisms and antiprisms really boring? I. Zbl 1050.51012
Grünbaum, Branko
2004
Relative distance and packing a body by homothetical copies. Zbl 1050.52007
Lángi, Zsolt; Lassak, Marek
2003
Empty monochromatic fourgons in two-colored point sets. Zbl 1062.52016
Brass, Peter
2004
Cover-up. Zbl 1057.52009
Conway, John H.; Soifer, Alexander
2004
Wild polyomino weak $$(1,2)$$-achievement games. Zbl 1060.05020
Sieben, Nándor
2004
Combinatorial games: modular $$n$$-queen. Zbl 1061.05023
Khan, Samee Ullah
2003
The odd-distance graph. Zbl 1277.05072
Rosenfeld, Moshe
2013
Progress in my favorite open problem of mathematics, chromatic number of the plane: an Étude in five movements. Zbl 1403.05157
Soifer, Alexander
2018
A note on the clique chromatic number of geometric graphs. Zbl 1407.05091
Fox, Jacob; Pach, János; Suk, Andrew
2018
A generalized isodiametric problem. Zbl 1352.51012
Pelekis, Christos
2016
A very short proof of a well-known fact about circles in the plane. Zbl 1351.51014
Johnson, Peter; Noble, Matt
2015
Weighted Erdős-Mordell inequality for star-shaped polygons. Zbl 1352.51017
Rosenfeld, Moshe; Tan, Tran Nhat
2015
Graphs with no grid obstacle representation. Zbl 1352.05133
Pach, János
2016
Packing clones in convex figures. Zbl 0927.52025
Soifer, Alexander
1998
Duplicated distances in subsets of finite planar sets. Zbl 0941.52014
Erdős, Paul; Fishburn, Peter
1999
The chromatic numbers of some Euclidean distance graphs. Zbl 0990.05048
Bohannon, Aaron; Johnson, Peter; Lanig, Jeremy; Rubalcaba, Robert
2001
A convex polyhedron which is not equifacettable. Zbl 0998.52007
Grünbaum, Branko
2001
Yet another species of forbidden-distances chromatic number. Zbl 0979.05051
Abrams, Aaron; Johnson, Peter
2001
Problems on approximation by triangles. Zbl 0989.52005
Braß, Peter; Lassak, Marek
2001
Convex isosceles triangle polyhedra. Zbl 0983.52007
Malkevitch, Joseph
2001
Cutting circles into equal area pieces. Zbl 0993.51005
Bose, Prosenjit; Czyzowicz, Jurek; Kranakis, Evangelos; Krizanc, Danny; Maheshwari, Anil
2001
A starshaped polyhedron with no net. Zbl 0998.52008
Grünbaum, Branko
2001
A buttressed octahedron. Zbl 1001.52007
Robertson, Lew; Schweitzer, Michael; Wagon, Stan
2002
Minimum saturated packings of congruent integer triangles. Zbl 0971.52014
Harborth, Heiko; Möller, Meinhard
1999
Which $$(n_4)$$ configurations exist? Zbl 0964.51011
Grünbaum, Branko
2000
On an Erdős problem for distinct distances in convex polygons. Zbl 1112.52300
Fishburn, Peter
2000
Connected (n4) configurations exist for almost all n. Zbl 0966.51012
Grünbaum, Branko
2000
Odd polyhedra. Zbl 0843.52008
Grünbaum, Branko
1991
Relatives of chromatic number of the plane. I. Zbl 0853.05039
Soifer, Alexander
1992
The fractional chromatic number of the plane. Zbl 0843.05043
Fisher, David; Ullman, Daniel
1992
Functions which preserve unit distance. Zbl 0844.51007
Greenwell, Don; Johnson, Peter D. jun.
1993
A large independent set in the unit distance graph. Zbl 0847.05048
Hochberg, Robert; O’Donnell, Paul
1993
Is the four color theorem true? Zbl 0854.05045
Kainen, Paul C.
1993
About a problem concerning functions which preserve unit distance. Zbl 0844.51008
Kuz’minykh, Alexandr V.
1994
Six-realizable set $$X_ 6$$. Zbl 0845.05039
Soifer, Alexander
1994
Quadrangles, pentagons, and computers, revisited. Zbl 0845.51014
Grünbaum, Branko
1994
On the chromatic number of circular disks and infinite strips in the plane. Zbl 1466.05215
Polymath, D. H. J.
2021
Polyiamonds attaining extremal topological properties. I. Zbl 1458.52012
Malen, Greg; Roldán, Érika
2020
Graph minimization, focusing on the example of 5-chromatic unit-distance graphs in the plane. Zbl 1452.05070
Parts, Jaan
2020
Tiling the plane with equilateral triangles. Zbl 1430.52027
Pach, János; Tardos, Gábor
2019
Polyominoes with maximally many holes. Zbl 1428.05052
Kahle, Matthew; Roldán, Érika
2019
The chromatic number of the plane is at least. Zbl 1404.05063
de Grey, Aubrey D. N. J.
2018
Computing small unit-distance graphs with chromatic number 5. Zbl 1404.05054
Heule, Marijn J. H.
2018
Progress in my favorite open problem of mathematics, chromatic number of the plane: an Étude in five movements. Zbl 1403.05157
Soifer, Alexander
2018
A note on the clique chromatic number of geometric graphs. Zbl 1407.05091
Fox, Jacob; Pach, János; Suk, Andrew
2018
The edge Folkman number $$F_e(3,3;4)$$ is greater than 19. Zbl 1373.05116
Bikov, Aleksandar; Nenov, Nedyalko
2017
A unit distance graph in the plane with fractional chromatic number 383/102. Zbl 1360.05032
Exoo, Geoffrey; Ismailescu, Dan
2017
A generalized isodiametric problem. Zbl 1352.51012
Pelekis, Christos
2016
Graphs with no grid obstacle representation. Zbl 1352.05133
Pach, János
2016
New lower bounds on $$\chi ({\mathbb R}^d)$$ for $$d = 8,\dots, 12$$. Zbl 1327.05247
Kahle, Matthew; Taha, Birra
2015
Coloring distance graphs: a few answers and many questions. Zbl 1334.05039
Kloeckner, Benoît R.
2015
A very short proof of a well-known fact about circles in the plane. Zbl 1351.51014
Johnson, Peter; Noble, Matt
2015
Weighted Erdős-Mordell inequality for star-shaped polygons. Zbl 1352.51017
Rosenfeld, Moshe; Tan, Tran Nhat
2015
Ordered black boxes: existence. Zbl 1314.03042
Shelah, Saharon
2014
Geometric realization of toroidal quadrangulations without hidden symmetries. Zbl 1312.51007
Lawrencenko, Serge
2014
Multiplication in Newton’s Principia and Jordan-Banach algebras. II. Zbl 1327.46069
Wawrzycki, Jarosław
2014
The odd-distance graph. Zbl 1277.05072
Rosenfeld, Moshe
2013
Tiling a unit square with 8 squares. Zbl 1268.52018
Praton, Iwan
2013
Bounds for covers of unit arcs. Zbl 1273.52012
Wetzel, John E.
2013
Tangled thrackles. Zbl 1272.05034
2012
The best polynomial bounds for the number of triangles in a simple arrangement of $$n$$ pseudo-lines. Zbl 1335.52032
Blanc, Jérémy
2011
On the chromatic number of real and rational spaces. Zbl 1190.05067
Cibulka, Josef
2008
A note on convex realizability of arrangements of pseudocircles. Zbl 1159.52022
Linhart, Johann; Ortner, Ronald
2008
Tromino tiling deficient cubes of side length $$2^n$$. Zbl 1184.05020
Starr, Norton
2008
Note on covering square with equal squares. Zbl 1162.52011
Karabash, Dmytro; Soifer, Alexander
2008
Equidecomposability (scissors congruence) of polyhedra in $$\mathbb R^3$$ and $$\mathbb R^4$$ is algorithmically decidable: Hilbert’s 3rd problem revisited. Zbl 1161.52011
2008
Comment on Fox news. Zbl 1145.05020
Pach, János; Tóth, Géza
2006
Covering squares with unit squares. Zbl 1097.52005
Friedman, Erich; Paterson, David A.
2006
Are prisms and antiprisms really boring? III. Zbl 1094.52007
Grünbaum, Branko
2005
Examples on the plane and $$R^n$$. Zbl 1057.03037
Soifer, Alexander; Shelah, Saharon
2004
30 two-colored points with no empty monochromatic convex fourgons. Zbl 1063.52011
Friedman, Erich
2004
Are prisms and antiprisms really boring? I. Zbl 1050.51012
Grünbaum, Branko
2004
Empty monochromatic fourgons in two-colored point sets. Zbl 1062.52016
Brass, Peter
2004
Cover-up. Zbl 1057.52009
Conway, John H.; Soifer, Alexander
2004
Wild polyomino weak $$(1,2)$$-achievement games. Zbl 1060.05020
Sieben, Nándor
2004
Chromatic number of the plane and its relatives. Zbl 1035.05043
Soifer, Alexander
2003
Midpoints of segments induced by a point set. Zbl 1060.11015
Pach, János
2003
On four points of a convex body in large relative distances. Zbl 1061.52001
Lángi, Zsolt; Lassak, Marek
2003
Chromatic number of the plane and its relatives. II: Polychromatic number and 6-coloring. Zbl 1061.05038
Soifer, Alexander
2003
Open-ended configurations of radio telescopes: A geometrical analysis. Zbl 1142.85300
Kreinovich, Vladik; Starks, Scott A.; Iourinski, Dima; Kosheleva, Olga; Finkelstein, Andrei
2003
On the number of points at distance at least 1 in the unit cube. Zbl 1061.52003
Bálint, Vojtech; Bálint, Vojtech jun.
2003
(1-2-3)-complexes. Zbl 1045.52004
Grünbaum, Branko
2003
Hunting unit-distance graphs in rational $$n$$-spaces. Zbl 1054.05041
Mann, Matthias
2003
Relative distance and packing a body by homothetical copies. Zbl 1050.52007
Lángi, Zsolt; Lassak, Marek
2003
Combinatorial games: modular $$n$$-queen. Zbl 1061.05023
Khan, Samee Ullah
2003
Connected $$(n_4)$$ configurations exist for almost all $$n$$ – an update. Zbl 1116.52302
Grünbaum, Branko
2002
No-net polyhedra. Zbl 1010.52010
Grünbaum, Branko
2002
Squares touching a constant number of other squares. Zbl 1041.52009
Friedman, Erich
2002
A buttressed octahedron. Zbl 1001.52007
Robertson, Lew; Schweitzer, Michael; Wagon, Stan
2002
On polygons enclosing point sets. Zbl 1004.52001
Czyzowicz, Jurek; Hurtado, Ferran; Urrutia, Jorge; Zaguia, Nejib
2001
A relative of “Napoleon’s theorem”. Zbl 0979.51008
Grünbaum, Branko
2001
The chromatic numbers of some Euclidean distance graphs. Zbl 0990.05048
Bohannon, Aaron; Johnson, Peter; Lanig, Jeremy; Rubalcaba, Robert
2001
A convex polyhedron which is not equifacettable. Zbl 0998.52007
Grünbaum, Branko
2001
Yet another species of forbidden-distances chromatic number. Zbl 0979.05051
Abrams, Aaron; Johnson, Peter
2001
Problems on approximation by triangles. Zbl 0989.52005
Braß, Peter; Lassak, Marek
2001
Convex isosceles triangle polyhedra. Zbl 0983.52007
Malkevitch, Joseph
2001
Cutting circles into equal area pieces. Zbl 0993.51005
Bose, Prosenjit; Czyzowicz, Jurek; Kranakis, Evangelos; Krizanc, Danny; Maheshwari, Anil
2001
A starshaped polyhedron with no net. Zbl 0998.52008
Grünbaum, Branko
2001
Colorings of metric spaces. Zbl 0951.05037
Benda, M.; Perles, M.
2000
Thirteen problems on crossing numbers. Zbl 0957.05026
Pach, János; Tóth, Géza
2000
A Ramsey-type theorem for bipartite graphs. Zbl 0978.05052
Erdős, Paul; Hajnal, András; Pach, János
2000
Arbitrary girth, 4-chromatic unit distance graphs in the plane.  I: Graph description. Zbl 0937.05038
O&rsquo;Donnell, Paul
2000
Arbitrary girth, 4-chromatic unit distance graphs in the plane. II: Graph embedding. Zbl 0979.05045
O&rsquo;Donnell, Paul
2000
Astral $$(n_4)$$ configurations. Zbl 0981.51014
Grünbaum, Branko
2000
Ahn, Hee-Kap; Bose, Prosenjit; Czyzowicz, Jurek; Hanusse, Nicolas; Kranakis, Evangelos; Morin, Pat
2000
Which $$(n_4)$$ configurations exist? Zbl 0964.51011
Grünbaum, Branko
2000
On an Erdős problem for distinct distances in convex polygons. Zbl 1112.52300
Fishburn, Peter
2000
Connected (n4) configurations exist for almost all n. Zbl 0966.51012
Grünbaum, Branko
2000
Monochromatic intersection points in families of colored lines. Zbl 0948.52013
Grünbaum, Branko
1999
The search for symmetric Venn diagrams. Zbl 0929.52007
Grünbaum, Branko
1999
More on the fractional chromatic number. Zbl 0941.05024
Johnson, P. D. jun.
1999
Duplicated distances in subsets of finite planar sets. Zbl 0941.52014
Erdős, Paul; Fishburn, Peter
1999
Minimum saturated packings of congruent integer triangles. Zbl 0971.52014
Harborth, Heiko; Möller, Meinhard
1999
Packing clones in convex figures. Zbl 0927.52025
Soifer, Alexander
1998
Folding and turning along geodesics in a convex surface. Zbl 0892.52004
Pach, János
1997
Astrogeometry: Geometry explains shapes of celestial bodies. Zbl 0885.70011
Finkelstein, Andrei; Kosheleva, Olga; Kreinovich, Vladik
1997
Embedding graphs in Euclidean spaces, an exploration guided by Paul Erdös. Zbl 0881.05039
Nešetřil, Jaroslav; Rosenfeld, Moshe
1997
On the independence number of coin graphs. Zbl 0853.05051
Pach, János; Tóth, Géza
1996
Some 4-chromatic unit-distance graphs without small cycles. Zbl 0855.05056
Hochberg, Robert; O&rsquo;Donnell, Paul
1996
Odd integral distances among points in the plane. Zbl 0844.52010
Rosenfeld, Moshe
1996
Lower bounds on the independence number. Zbl 0972.05024
Bertram, Edward; Horák, Peter
1996
About two definitions of the fractional chromatic number. Zbl 0856.05036
Johnson, P. D. jun.
1996
Snaky is an edge-to-edge looser. Zbl 0854.90141
Harborth, Heiko; Seemann, Markus
1996
How to measure arbitrary distances using a given standard length (i.e., a stick with two marks on it): It is necessary, it is theoretically possible, it is feasible. Zbl 0848.51009
1996
Space-time is “square times” more difficult to approximate than Euclidean space. Zbl 0966.51017
1996
Choosability versus chromaticity—the plane unit distance graph has a $$2$$-chromatic subgraph of infinite list-chromatic number. Zbl 0855.05055
Jensen, Tommy R.; Toft, Bjarne
1995
The list-chromatic number of Euclidean space. Zbl 0847.05056
Schmerl, James H.
1995
Which algorithms are feasible and which are not depends on the geometry of space-time. Zbl 0844.68060
1995
How to convexify a polygon. Zbl 0866.52001
Grünbaum, Branko
1995
Squares in a square. Zbl 0850.52013
Erdős, Paul; Soifer, Alexander
1995
Unit-distance preserving theorem is logically non-trivial. Zbl 0900.03060
1995
Uniform tilings of $$3$$-space. Zbl 0844.52022
Grünbaum, Branko
1994
Hamiltonian polygons and polyhedra. Zbl 0845.05066
Grünbaum, Branko
1994
The choice number of the plane. Zbl 0848.05031
Johnson, Peter D. jun.
1994
About a problem concerning functions which preserve unit distance. Zbl 0844.51008
Kuz&rsquo;minykh, Alexandr V.
1994
Six-realizable set $$X_ 6$$. Zbl 0845.05039
Soifer, Alexander
1994
...and 16 more Documents
all top 5

#### Cited by 408 Authors

 20 Pach, János 19 Raĭgorodskiĭ, Andreĭ Mikhaĭlovich 12 Fox, Jacob 7 Kreinovich, Vladik Yakovlevich 7 Tóth, Géza 5 Dumitrescu, Adrian 5 Hocquard, Hervé 5 Raspaud, André 5 Sagdeev, A. A. 5 Shelah, Saharon 5 Soifer, Alexander 4 Johnson, Peter D. jun. 4 Kupavskii, Andrey 4 Montassier, Mickaël 4 Su, Zhanjun 4 Tomon, István 3 Aichholzer, Oswin 3 Berman, Leah Wrenn 3 Boben, Marko 3 Bokowski, Jürgen G. 3 Demidovich, Yu. A. 3 Graham, Ronald Lewis 3 Grünbaum, Branko 3 Kosheleva, Olga M. 3 O’Rourke, Joseph 3 Pinchasi, Rom 3 Pisanski, Tomaž 3 Przybyło, Jakub 3 Richter, Christian 3 Rubanov, O. I. 3 Sudakov, Benny 3 Tóth, Csaba D. 3 Toussaint, Godfried T. 3 Urrutia Galicia, Jorge L. 2 Ábrego, Bernardo Manuel 2 Alon, Noga M. 2 Befumo, Arthur 2 Bikov, Aleksandar 2 Bousquet, Nicolas 2 Cherkashin, Danila D. 2 Chung Graham, Fan-Rong King 2 Damian, Mirela 2 Deza, Michel Marie 2 Ding, Ren 2 Exoo, Geoffrey 2 Faudree, Jill R. 2 Fernández-Merchant, Silvia 2 Fulek, Radoslav 2 Ghomi, Mohammad 2 Grytczuk, Jarosław 2 Hurtado, Ferran 2 Ismailescu, Dan P. 2 Junosza-Szaniawski, Konstanty 2 Komjáth, Péter 2 Kyncl, Jan 2 Lagoutte, Aurélie 2 Lan, Wenhua 2 Lenchner, Jonathan 2 Li, Sipeng 2 Liang, Meilian 2 Mabry, Rick 2 Mamakani, Khalegh 2 Margenstern, Maurice 2 Matoušek, Jiří 2 Mitricheva, I. M. 2 Nenov, Nedyalko Dimov 2 Oliveros, Deborah 2 Pellicer, Daniel 2 Radziszowski, Stanisław P. 2 Rodger, Christopher Andrew 2 Rosenfeld, Moshe 2 Ruskey, Frank 2 Salazar, Gelasio 2 Samirov, D. V. 2 Scheucher, Manfred 2 Sharir, Micha 2 Shen, Jian 2 Sieben, Nándor 2 Sokół, Joanna 2 Stiebitz, Michael 2 Suk, Andrew 2 Székely, László A. 2 Thomassé, Stéphan 2 Wei, Xianglin 2 Węsek, Krzysztof 2 Xu, Xiaodong 2 Zapletal, Jindřich 1 Abbott, Timothy G. 1 Abel, Zachary R. 1 Abrams, Aaron 1 Adams, Francis 1 Agarwal, Pankaj Kumar 1 Ahn, Hee-Kap 1 Araiza, Roberto 1 Aranda, Andrés 1 Ardal, Hayri 1 Arnold, Maxim 1 Axenovich, Maria A. 1 Bae, Sang Won 1 Bald, Samuel ...and 308 more Authors
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#### Cited in 65 Journals

 31 Discrete Mathematics 31 Discrete & Computational Geometry 18 Discrete Applied Mathematics 14 Mathematical Notes 11 Journal of Combinatorial Theory. Series A 11 European Journal of Combinatorics 10 Graphs and Combinatorics 10 Journal of Mathematical Sciences (New York) 8 Journal of Combinatorial Theory. Series B 6 Theoretical Computer Science 6 Computational Geometry 5 Israel Journal of Mathematics 5 SIAM Journal on Discrete Mathematics 4 Mathematics Magazine 4 The Electronic Journal of Combinatorics 3 International Journal of Theoretical Physics 3 Problems of Information Transmission 3 Journal of Geometry 3 Journal of Graph Theory 3 Proceedings of the American Mathematical Society 2 Periodica Mathematica Hungarica 2 The Mathematical Intelligencer 2 Advances in Mathematics 2 Geometriae Dedicata 2 Journal of Computer and System Sciences 2 Acta Mathematica Hungarica 2 Order 2 Random Structures & Algorithms 2 Elemente der Mathematik 2 St. Petersburg Mathematical Journal 2 Sbornik: Mathematics 2 Journal of Combinatorial Optimization 1 American Mathematical Monthly 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Journal d’Analyse Mathématique 1 Beiträge zur Algebra und Geometrie 1 The Annals of Probability 1 Applied Mathematics and Computation 1 Canadian Mathematical Bulletin 1 Manuscripta Mathematica 1 Results in Mathematics 1 Transactions of the American Mathematical Society 1 Acta Mathematicae Applicatae Sinica. English Series 1 Optimization 1 Algorithmica 1 International Journal of Approximate Reasoning 1 Applied Mathematics Letters 1 Godishnik na Sofiĭskiya Universitet “Sv. Kliment Okhridski”. Fakultet po Matematika i Informatika 1 Aequationes Mathematicae 1 Archive for Mathematical Logic 1 The Australasian Journal of Combinatorics 1 Topological Methods in Nonlinear Analysis 1 Discussiones Mathematicae. Graph Theory 1 Reliable Computing 1 Theory of Computing Systems 1 Vietnam Journal of Mathematics 1 Geometry & Topology 1 Journal of Graph Algorithms and Applications 1 Advances in Geometry 1 Journal of Applied Mathematics and Computing 1 Journal of Discrete Algorithms 1 Sibirskie Èlektronnye Matematicheskie Izvestiya 1 The College Mathematics Journal 1 Forum of Mathematics, Sigma 1 PUMP Journal of Undergraduate Research
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#### Cited in 34 Fields

 180 Combinatorics (05-XX) 78 Convex and discrete geometry (52-XX) 29 Geometry (51-XX) 25 Computer science (68-XX) 9 Mathematical logic and foundations (03-XX) 8 Order, lattices, ordered algebraic structures (06-XX) 6 Differential geometry (53-XX) 6 Manifolds and cell complexes (57-XX) 6 Numerical analysis (65-XX) 4 History and biography (01-XX) 4 Number theory (11-XX) 4 Probability theory and stochastic processes (60-XX) 4 Operations research, mathematical programming (90-XX) 3 Group theory and generalizations (20-XX) 3 Measure and integration (28-XX) 3 General topology (54-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Algebraic geometry (14-XX) 2 Relativity and gravitational theory (83-XX) 2 Biology and other natural sciences (92-XX) 1 General and overarching topics; collections (00-XX) 1 Field theory and polynomials (12-XX) 1 Commutative algebra (13-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Real functions (26-XX) 1 Potential theory (31-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Algebraic topology (55-XX) 1 Statistics (62-XX) 1 Quantum theory (81-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Astronomy and astrophysics (85-XX) 1 Mathematics education (97-XX)