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Kainen, Paul C.

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Author ID: kainen.paul-c Recent zbMATH articles by "Kainen, Paul C."
Published as: Kainen, P. C.; Kainen, Paul; Kainen, Paul C.
Documents Indexed: 74 Publications since 1968, including 1 Book

Publications by Year

Citations contained in zbMATH

49 Publications have been cited 353 times in 279 Documents Cited by Year
The book thickness of a graph. Zbl 0427.05028
Bernhart, Frank; Kainen, Paul C.
87
1979
The four-color problem. Assaults and conquest. Zbl 0463.05041
Saaty, Thomas L.; Kainen, Paul C.
48
1977
Toroidal graphs with arbitrarily high crossing numbers. Zbl 0285.05104
Harary, Frank; Kainen, Paul C.; Schwenk, Allen J.
23
1973
Complexity of Gaussian-radial-basis networks approximating smooth functions. Zbl 1162.65006
Kainen, Paul C.; Kůrková, Věra; Sanguineti, Marcello
14
2009
An integral upper bound for neural network approximation. Zbl 1186.68370
Kainen, Paul C.; Kůrková, Věra
13
2009
A lower bound for crossing numbers of graphs with application to \(K_n\),\(K_{pq}\)g, and \(Q(d)\). Zbl 0237.05104
Kainen, Paul C.
12
1972
The book thickness of a graph. II. Zbl 0749.05030
Kainen, Paul C.
11
1990
Thickness and coarseness of graphs. Zbl 0264.05108
Kainen, Paul C.
10
1973
Weak adjoint functors. Zbl 0209.04503
Kainen, P. C.
9
1971
A Sobolev-type upper bound for rates of approximation by linear combinations of Heaviside plane waves. Zbl 1119.41023
Kainen, Paul C.; Kurková, Věra; Vogt, Andrew
8
2007
Minimization of error functionals over variable-basis functions. Zbl 1061.49020
Kainen, Paul C.; Kurková, Vera; Sanguineti, Marcello
8
2003
On a problem of P. Erdős. Zbl 0182.57901
Kainen, Paul C.
8
1968
Dependence of computational models on input dimension: tractability of approximation and optimization tasks. Zbl 1365.68373
Kainen, Paul C.; Kůrková, Věra; Sanguineti, Marcello
7
2012
Geometry and topology of continuous best and near best approximations. Zbl 0969.41020
Kainen, Paul C.; Kůrková, Věra; Vogt, Andrew
7
2000
On stable crossing numbers. Zbl 0401.05039
Kainen, Paul C.; White, Arthur T.
7
1978
Quasiorthogonal dimension of Euclidean spaces. Zbl 0783.05030
Kainen, Paul C.; Kůrková, Věra
6
1993
A generalization of the 5-color theorem. Zbl 0293.05111
Kainen, Paul C.
6
1974
Extension of a theorem of Whitney. Zbl 1131.05035
Kainen, Paul C.; Overbay, Shannon
5
2007
Best approximation by linear combinations of characteristic functions of half-spaces. Zbl 1038.41011
Kainen, Paul C.; Kůrková, Věra; Vogt, Andrew
5
2003
On robust cycle bases. Zbl 1075.05555
Kainen, Paul C.
5
2002
Continuity of approximation by neural networks in \(L_p\) spaces. Zbl 1055.41020
Kainen, Paul C.; Kurková, Vera; Vogt, Andrew
4
2001
Chromatic number and skewness. Zbl 0298.05116
Kainen, Paul C.
4
1975
Some recent results in topological graph theory. Zbl 0319.05103
Kainen, Paul C.
4
1974
Universal coefficient theorems for generalized homology and stable cohomotopy. Zbl 0211.32704
Kainen, P. C.
4
1971
Cycle construction and geodesic cycles with application to the hypercube. Zbl 1329.05162
Kainen, Paul C.
3
2015
Replacing points by compacta in neural network approximation. Zbl 1075.54013
Kainen, Paul C.
3
2004
A maximal toroidal graph which is not a triangulation. Zbl 0271.05108
Harary, Frank; Kainen, P. C.; Schwenk, A. J.; White, A. T.
3
1973
On the stable crossing number of cubes. Zbl 0253.05118
Kainen, Paul C.
3
1972
Graph bases and diagram commutativity. Zbl 1395.05092
Hammack, Richard H.; Kainen, Paul C.
2
2018
Integral combinations of Heavisides. Zbl 1225.26029
Kainen, Paul C.; Kůrková, Věra; Vogt, Andrew
2
2010
Singularities of finite scaling functions. Zbl 0852.42020
Kůrková, V.; Kainen, P. C.
2
1996
Every commutative square of Abelian groups can be realized by a homotopy commutative square of Moore, or co-Moore, spaces. Zbl 0243.55007
Kainen, Paul C.
2
1972
Embeddings and orientations of graphs. Zbl 0247.05109
Kainen, Paul C.
2
1970
On 2-skeleta of Platonic polytopes. Zbl 1425.57002
Hammack, Richard; Kainen, Paul C.
1
2018
Robust cycle bases do not exist for \(K_{n, n}\) if \(n \geq 8\). Zbl 1375.05150
Hammack, Richard H.; Kainen, Paul C.
1
2018
Comparing fixed and variable-width Gaussian networks. Zbl 1343.68200
Kurková, Věra; Kainen, Paul C.
1
2014
Graph cycles and diagram commutativity. Zbl 1338.05135
Kainen, Paul C.
1
2012
Rates of minimization of error functionals over Boolean variable-basis functions. Zbl 1080.49020
Kainen, P. C.; Kurková, V.; Sanguineti, M.
1
2005
Isolated squares in hypercubes and robustness of commutativity. Zbl 1042.18007
Kainen, Paul C.
1
2002
Every graph of cyclic bandwidth 3 is toroidal. Zbl 0938.05025
Harary, Frank; Kainen, Paul C.; Riskin, Adrian
1
1999
Utilizing geometric anomalies of high dimension: When complexity makes computation easier. Zbl 0906.68126
Kainen, Paul C.
1
1997
Uniqueness of network parametrization and faster learning. Zbl 0938.68801
Kainen, Paul C.; Kůrková, Věra; Kreinovich, Vladik; Sirisaengtaksin, Ongard
1
1994
Is the four color theorem true? Zbl 0854.05045
Kainen, Paul C.
1
1993
The cube of a path is maximal planar. Zbl 0804.05046
Harary, Frank; Kainen, Paul C.
1
1993
Upper bound for linear arboricity. Zbl 0732.05020
Kainen, Paul C.
1
1991
Arboricity and edge partitions. Zbl 0763.05028
Kainen, Paul C.
1
1991
On triangular colorings of a planar graph. Zbl 0416.05041
Harary, Frank; Kainen, Paul C.
1
1977
Relative colorings of graphs. Zbl 0258.05108
Kainen, Paul C.
1
1973
Trivalent descriptions of graphs. Zbl 0288.05103
Kainen, Paul C.
1
1971
Graph bases and diagram commutativity. Zbl 1395.05092
Hammack, Richard H.; Kainen, Paul C.
2
2018
On 2-skeleta of Platonic polytopes. Zbl 1425.57002
Hammack, Richard; Kainen, Paul C.
1
2018
Robust cycle bases do not exist for \(K_{n, n}\) if \(n \geq 8\). Zbl 1375.05150
Hammack, Richard H.; Kainen, Paul C.
1
2018
Cycle construction and geodesic cycles with application to the hypercube. Zbl 1329.05162
Kainen, Paul C.
3
2015
Comparing fixed and variable-width Gaussian networks. Zbl 1343.68200
Kurková, Věra; Kainen, Paul C.
1
2014
Dependence of computational models on input dimension: tractability of approximation and optimization tasks. Zbl 1365.68373
Kainen, Paul C.; Kůrková, Věra; Sanguineti, Marcello
7
2012
Graph cycles and diagram commutativity. Zbl 1338.05135
Kainen, Paul C.
1
2012
Integral combinations of Heavisides. Zbl 1225.26029
Kainen, Paul C.; Kůrková, Věra; Vogt, Andrew
2
2010
Complexity of Gaussian-radial-basis networks approximating smooth functions. Zbl 1162.65006
Kainen, Paul C.; Kůrková, Věra; Sanguineti, Marcello
14
2009
An integral upper bound for neural network approximation. Zbl 1186.68370
Kainen, Paul C.; Kůrková, Věra
13
2009
A Sobolev-type upper bound for rates of approximation by linear combinations of Heaviside plane waves. Zbl 1119.41023
Kainen, Paul C.; Kurková, Věra; Vogt, Andrew
8
2007
Extension of a theorem of Whitney. Zbl 1131.05035
Kainen, Paul C.; Overbay, Shannon
5
2007
Rates of minimization of error functionals over Boolean variable-basis functions. Zbl 1080.49020
Kainen, P. C.; Kurková, V.; Sanguineti, M.
1
2005
Replacing points by compacta in neural network approximation. Zbl 1075.54013
Kainen, Paul C.
3
2004
Minimization of error functionals over variable-basis functions. Zbl 1061.49020
Kainen, Paul C.; Kurková, Vera; Sanguineti, Marcello
8
2003
Best approximation by linear combinations of characteristic functions of half-spaces. Zbl 1038.41011
Kainen, Paul C.; Kůrková, Věra; Vogt, Andrew
5
2003
On robust cycle bases. Zbl 1075.05555
Kainen, Paul C.
5
2002
Isolated squares in hypercubes and robustness of commutativity. Zbl 1042.18007
Kainen, Paul C.
1
2002
Continuity of approximation by neural networks in \(L_p\) spaces. Zbl 1055.41020
Kainen, Paul C.; Kurková, Vera; Vogt, Andrew
4
2001
Geometry and topology of continuous best and near best approximations. Zbl 0969.41020
Kainen, Paul C.; Kůrková, Věra; Vogt, Andrew
7
2000
Every graph of cyclic bandwidth 3 is toroidal. Zbl 0938.05025
Harary, Frank; Kainen, Paul C.; Riskin, Adrian
1
1999
Utilizing geometric anomalies of high dimension: When complexity makes computation easier. Zbl 0906.68126
Kainen, Paul C.
1
1997
Singularities of finite scaling functions. Zbl 0852.42020
Kůrková, V.; Kainen, P. C.
2
1996
Uniqueness of network parametrization and faster learning. Zbl 0938.68801
Kainen, Paul C.; Kůrková, Věra; Kreinovich, Vladik; Sirisaengtaksin, Ongard
1
1994
Quasiorthogonal dimension of Euclidean spaces. Zbl 0783.05030
Kainen, Paul C.; Kůrková, Věra
6
1993
Is the four color theorem true? Zbl 0854.05045
Kainen, Paul C.
1
1993
The cube of a path is maximal planar. Zbl 0804.05046
Harary, Frank; Kainen, Paul C.
1
1993
Upper bound for linear arboricity. Zbl 0732.05020
Kainen, Paul C.
1
1991
Arboricity and edge partitions. Zbl 0763.05028
Kainen, Paul C.
1
1991
The book thickness of a graph. II. Zbl 0749.05030
Kainen, Paul C.
11
1990
The book thickness of a graph. Zbl 0427.05028
Bernhart, Frank; Kainen, Paul C.
87
1979
On stable crossing numbers. Zbl 0401.05039
Kainen, Paul C.; White, Arthur T.
7
1978
The four-color problem. Assaults and conquest. Zbl 0463.05041
Saaty, Thomas L.; Kainen, Paul C.
48
1977
On triangular colorings of a planar graph. Zbl 0416.05041
Harary, Frank; Kainen, Paul C.
1
1977
Chromatic number and skewness. Zbl 0298.05116
Kainen, Paul C.
4
1975
A generalization of the 5-color theorem. Zbl 0293.05111
Kainen, Paul C.
6
1974
Some recent results in topological graph theory. Zbl 0319.05103
Kainen, Paul C.
4
1974
Toroidal graphs with arbitrarily high crossing numbers. Zbl 0285.05104
Harary, Frank; Kainen, Paul C.; Schwenk, Allen J.
23
1973
Thickness and coarseness of graphs. Zbl 0264.05108
Kainen, Paul C.
10
1973
A maximal toroidal graph which is not a triangulation. Zbl 0271.05108
Harary, Frank; Kainen, P. C.; Schwenk, A. J.; White, A. T.
3
1973
Relative colorings of graphs. Zbl 0258.05108
Kainen, Paul C.
1
1973
A lower bound for crossing numbers of graphs with application to \(K_n\),\(K_{pq}\)g, and \(Q(d)\). Zbl 0237.05104
Kainen, Paul C.
12
1972
On the stable crossing number of cubes. Zbl 0253.05118
Kainen, Paul C.
3
1972
Every commutative square of Abelian groups can be realized by a homotopy commutative square of Moore, or co-Moore, spaces. Zbl 0243.55007
Kainen, Paul C.
2
1972
Weak adjoint functors. Zbl 0209.04503
Kainen, P. C.
9
1971
Universal coefficient theorems for generalized homology and stable cohomotopy. Zbl 0211.32704
Kainen, P. C.
4
1971
Trivalent descriptions of graphs. Zbl 0288.05103
Kainen, Paul C.
1
1971
Embeddings and orientations of graphs. Zbl 0247.05109
Kainen, Paul C.
2
1970
On a problem of P. Erdős. Zbl 0182.57901
Kainen, Paul C.
8
1968
all top 5

Cited by 412 Authors

22 Kainen, Paul C.
15 Kůrková, Věra
15 Sanguineti, Marcello
10 Gnecco, Giorgio
10 Liotta, Giuseppe
9 Costarelli, Danilo
9 Jendrol’, Stanislav
6 Czap, Július
6 Di Giacomo, Emilio
5 Klešč, Marián
5 Salazar, Gelasio
5 Székely, László A.
5 Vinti, Gianluca
5 Wood, David Ronald
4 Bekos, Michael A.
4 Hammack, Richard H.
4 Hartung, Elizabeth J.
4 Sýkora, Ondrej
4 Vogt, Andrew
4 Vrto, Imrich
4 Wismath, Stephen K.
3 Alessandri, Angelo
3 Auer, Christopher
3 Beineke, Lowell W.
3 Binucci, Carla
3 Brandenburg, Franz-Josef
3 Cimikowski, Robert J.
3 Fabrici, Igor
3 Gleißner, Andreas
3 Hasunuma, Toru
3 Hong, Seok-Hee
3 Kaufmann, Michael
3 Kobourov, Stephen G.
3 Montecchiani, Fabrizio
3 Raftopoulou, Chrysanthi N.
3 Širáň, Jozef
3 Spigler, Renato
3 Tóth, Csaba D.
3 Voigt, Margit
2 Ábrego, Bernardo Manuel
2 Albertson, Michael O.
2 Alfaro Montúfar, Carlos Alejandro
2 Arroyo, Alan
2 Bachmaier, Christian
2 Bernhart, Frank R.
2 Bruckdorfer, Till
2 Cao, Feilong
2 Chia, Gek-Ling
2 Czumaj, Artur
2 Derňár, Marek
2 Didimo, Walter
2 Dujmović, Vida
2 Duncan, Christian A.
2 Eliahou, Shalom
2 Enomoto, Hikoe
2 Fernández-Merchant, Silvia
2 Fulek, Radoslav
2 Gaggero, Mauro
2 Garcia, Alfredo Daniel
2 Gibbons, Alan M.
2 Gorban, Alexander N.
2 Graver, Jack E.
2 Gronemann, Martin
2 Harary, Frank
2 Haythorpe, Michael
2 He, Meng
2 Heath, Lenwood S.
2 Hurtado, Ferran
2 Kauffman, Louis Hirsch
2 Korman, Matias
2 Kozyrev, V. P.
2 Kwiatkowska, Anna Beata
2 Meijer, Henk G.
2 Meng, Jixiang
2 Mohar, Bojan
2 Nakamoto, Atsuhiro
2 Nešetřil, Jaroslav
2 Newcombe, Alex
2 Nowakowski, Richard J.
2 Nozawa, Takayuki
2 Ota, Katsuhiro
2 Overbay, Shannon
2 Richter, Robert Bruce
2 Saleur, Hubert
2 Schäfer, Marcus
2 Shahrokhi, Farhad
2 Shibata, Yukio
2 Stadler, Peter F.
2 Stöhr, Elena A.
2 Syslo, Maciej M.
2 Thomassen, Carsten
2 Tyukin, Ivan Yu.
2 Vrbjarová, Michaela
2 Whitesides, Sue H.
2 Yannakakis, Mihalis
2 Zhao, Bin
1 Abbasi, Naser
1 Adamsson, Jay
1 Aichholzer, Oswin
1 Alam, Jawaherul Md.
...and 312 more Authors
all top 5

Cited in 96 Serials

29 Discrete Mathematics
25 Discrete Applied Mathematics
16 Journal of Combinatorial Theory. Series B
13 Computational Geometry
10 Algorithmica
9 Neural Networks
7 Information Processing Letters
7 Journal of Optimization Theory and Applications
7 Theoretical Computer Science
6 Journal of Approximation Theory
5 Journal of Graph Algorithms and Applications
4 Journal of Combinatorial Theory. Series A
4 Graphs and Combinatorics
4 Applied Mathematics Letters
4 SIAM Journal on Discrete Mathematics
3 Bulletin of Mathematical Biology
3 Information Sciences
3 Journal of Soviet Mathematics
3 Mathematische Nachrichten
3 European Journal of Combinatorics
3 Journal of Mathematical Chemistry
3 Journal of Discrete Algorithms
3 The Art of Discrete and Applied Mathematics
2 Communications in Mathematical Physics
2 Journal of Mathematical Analysis and Applications
2 Periodica Mathematica Hungarica
2 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
2 Applied Mathematics and Computation
2 Journal of Graph Theory
2 Journal of Pure and Applied Algebra
2 Proceedings of the American Mathematical Society
2 Quaestiones Mathematicae
2 Rendiconti del Seminario Matemàtico e Fisico di Milano
2 Results in Mathematics
2 Topology and its Applications
2 SIAM Journal on Algebraic and Discrete Methods
2 Discrete & Computational Geometry
2 Neural Computation
2 Journal of Knot Theory and its Ramifications
2 The Electronic Journal of Combinatorics
1 American Mathematical Monthly
1 Bulletin of the Australian Mathematical Society
1 Computers & Mathematics with Applications
1 Journal of the Franklin Institute
1 Chaos, Solitons and Fractals
1 The Mathematical Intelligencer
1 BIT
1 Fuzzy Sets and Systems
1 Glasgow Mathematical Journal
1 Integral Equations and Operator Theory
1 Journal of Computational and Applied Mathematics
1 Journal of Computer and System Sciences
1 Kybernetika
1 Mathematica Slovaca
1 Mathematical Systems Theory
1 Mathematische Zeitschrift
1 Osaka Journal of Mathematics
1 Ricerche di Matematica
1 Combinatorica
1 Chinese Annals of Mathematics. Series B
1 Order
1 Information and Computation
1 Journal of Parallel and Distributed Computing
1 Machine Learning
1 International Journal of Computational Geometry & Applications
1 International Journal of Algebra and Computation
1 MSCS. Mathematical Structures in Computer Science
1 European Journal of Operational Research
1 Historia Mathematica
1 Expositiones Mathematicae
1 The Australasian Journal of Combinatorics
1 Computational Optimization and Applications
1 Applied Categorical Structures
1 Applied and Computational Harmonic Analysis
1 Opuscula Mathematica
1 Theory and Applications of Categories
1 Discussiones Mathematicae. Graph Theory
1 Journal of Heuristics
1 INFORMS Journal on Computing
1 Optimization Methods & Software
1 Chicago Journal of Theoretical Computer Science
1 Journal of Discrete Mathematical Sciences & Cryptography
1 Acta Mathematica Sinica. English Series
1 Far East Journal of Mathematical Sciences
1 Algebraic & Geometric Topology
1 Miscelánea Matemática
1 Journal of Applied Mathematics
1 Journal of Machine Learning Research (JMLR)
1 JMMA. Journal of Mathematical Modelling and Algorithms
1 Cahiers de Topologie et Géométrie Différentielle Catégoriques
1 Journal of Statistical Mechanics: Theory and Experiment
1 Optimization Letters
1 Journal of Homotopy and Related Structures
1 Afrika Matematika
1 Computer Science Review
1 Bulletin of the Hellenic Mathematical Society
all top 5

Cited in 40 Fields

191 Combinatorics (05-XX)
71 Computer science (68-XX)
26 Approximations and expansions (41-XX)
21 Biology and other natural sciences (92-XX)
18 Operations research, mathematical programming (90-XX)
13 Category theory; homological algebra (18-XX)
12 Manifolds and cell complexes (57-XX)
9 Information and communication theory, circuits (94-XX)
7 Operator theory (47-XX)
7 Statistics (62-XX)
4 Order, lattices, ordered algebraic structures (06-XX)
4 Calculus of variations and optimal control; optimization (49-XX)
4 General topology (54-XX)
4 Algebraic topology (55-XX)
4 Numerical analysis (65-XX)
4 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
3 Mathematical logic and foundations (03-XX)
3 Group theory and generalizations (20-XX)
3 Integral transforms, operational calculus (44-XX)
3 Convex and discrete geometry (52-XX)
3 Probability theory and stochastic processes (60-XX)
2 History and biography (01-XX)
2 Number theory (11-XX)
2 Nonassociative rings and algebras (17-XX)
2 Harmonic analysis on Euclidean spaces (42-XX)
1 General and overarching topics; collections (00-XX)
1 Commutative algebra (13-XX)
1 Linear and multilinear algebra; matrix theory (15-XX)
1 Associative rings and algebras (16-XX)
1 \(K\)-theory (19-XX)
1 Real functions (26-XX)
1 Measure and integration (28-XX)
1 Partial differential equations (35-XX)
1 Integral equations (45-XX)
1 Functional analysis (46-XX)
1 Geometry (51-XX)
1 Classical thermodynamics, heat transfer (80-XX)
1 Quantum theory (81-XX)
1 Statistical mechanics, structure of matter (82-XX)
1 Systems theory; control (93-XX)

Citations by Year