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Dirac, Gabriel Andrew

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Author ID: dirac.gabriel-andrew Recent zbMATH articles by "Dirac, Gabriel Andrew"
Published as: Dirac, G. A.; Dirac, Gabriel; Dirac, Gabriel Andrew; Dirac, Gábor; Dirac, G.
Further Spellings: Dirac Gábor Endre
External Links: MGP · Wikidata · GND · IdRef
Documents Indexed: 68 Publications since 1951, including 3 Books
Biographic References: 4 Publications
Co-Authors: 6 Co-Authors with 6 Joint Publications
637 Co-Co-Authors

Publications by Year

Citations contained in zbMATH Open

53 Publications have been cited 1,768 times in 1,567 Documents Cited by Year
Some theorems on abstract graphs. Zbl 0047.17001
Dirac, G. A.
612
1952
On rigid circuit graphs. Zbl 0098.14703
Dirac, G. A.
377
1961
A property of 4-chromatic graphs and some remarks on critical graphs. Zbl 0046.41001
Dirac, G. A.
147
1952
In abstrakten Graphen vorhandene vollständige 4-Graphen und ihre Unterteilungen. Zbl 0096.17903
Dirac, Gabriel Andrew
102
1960
Minimally 2-connected graphs. Zbl 0153.25804
Dirac, G. A.
61
1967
A theorem of R. L. Brooks and a conjecture of H. Hadwiger. Zbl 0077.17002
Dirac, G. A.
43
1957
Homomorphism theorems for graphs. Zbl 0115.41005
Dirac, G. A.
32
1963
Some results concerning the structure of graphs. Zbl 0138.19203
Dirac, G. A.
32
1963
The structure of \(k\)-chromatic graphs. Zbl 0053.13102
Dirac, G. A.
29
1953
Map-colour theorems. Zbl 0047.42203
Dirac, G. A.
26
1952
A theorem of Kuratowski. Zbl 0055.17002
Dirac, G. A.; Schuster, S.
25
1954
Collinearity properties of sets of points. Zbl 0043.14602
Dirac, G. A.
24
1951
On the structure of 5- and 6-chromatic abstract graphs. Zbl 0131.38403
Dirac, G. A.
22
1964
Extensions of Menger’s theorem. Zbl 0112.38606
Dirac, G. A.
18
1963
Note on the colouring of graphs. Zbl 0043.38502
Dirac, G. A.
17
1951
The number of edges in critical graphs. Zbl 0298.05119
Dirac, G. A.
14
1974
On the maximal number of independent circuits in a graph. Zbl 0122.24903
Dirac, G.; Erdős, Pál
14
1963
4-chrome Graphen und vollständige 4-Graphen. Zbl 0096.17902
Dirac, Gabriel Andrew
13
1960
Map colour theorems related to the Heawood colour formula. Zbl 0071.17701
Dirac, G. A.
12
1956
Graphs in which every finite path is contained in a circuit. Zbl 0239.05129
Dirac, G. A.; Thomassen, C.
11
1973
Short proof of a map-colour theorem. Zbl 0077.36802
Dirac, G. A.
11
1957
Extensions of Turan’s theorem on graphs. Zbl 0113.24703
Dirac, G.
11
1963
Trennende Knotenpunktmengen und Reduzibilität abstrakter Graphen mit Anwendung auf das Vierfarbenproblem. Zbl 0096.17901
Dirac, G. A.
10
1960
Short proof of Menger’s graph theorem. Zbl 0144.45102
Dirac, G. A.
9
1966
On the structure of k-chromatic graphs. Zbl 0161.20704
Dirac, G. A.
9
1967
On the maximal number of independent triangles in graphs. Zbl 0111.35901
Dirac, G. A.
9
1963
Note on a problem in additive number theory. Zbl 0043.04702
Dirac, G. A.
8
1951
Généralisations du théorème de Menger. Zbl 0095.37803
Dirac, Gábor
7
1960
On Hamilton circuits and Hamilton paths. Zbl 0222.05114
Dirac, G. A.
6
1972
The colouring of maps. Zbl 0051.14702
Dirac, G. A.
6
1953
On the four-colour conjecture. Zbl 0112.15002
Dirac, G. A.
5
1963
Hamilton circuits and long circuits. Zbl 0376.05035
Dirac, G. A.
4
1978
Circuits in critical graphs. Zbl 0065.39001
Dirac, G. A.
4
1955
On separating sets and Menger’s theorem. Zbl 0251.05124
Dirac, Gabriel
3
1973
On arbitrarily traceable graphs. Zbl 0259.05119
Dirac, Gabriel
3
1973
Structural properties and circuits in graphs. Zbl 0322.05131
Dirac, G. A.
3
1976
Map colour theorems related to the Heawood colour formula. II. Zbl 0078.16503
Dirac, G. A.
3
1957
Paths and circuits in graphs: Extreme cases. Zbl 0090.39305
Dirac, G. A.
3
1959
A contraction theorem for abstract graphs. Zbl 0107.17301
Dirac, G. A.
3
1961
An extremal result for graphs with an application to their colourings. Zbl 0298.05117
Dirac, G. A.; Sorensen, B. Aagaard; Toft, B.
2
1974
Ovals with equichordal points. Zbl 0047.15804
Dirac, G. A.
2
1952
Corrigendum. A theorem of Kuratowski. Zbl 0098.36606
Dirac, G. A.; Schuster, S.
2
1961
Percy John Heawood (1861-1955). Zbl 0112.00305
Dirac, G. A.
2
1963
Graph union and chromatic number. Zbl 0126.39303
Dirac, G. A.
2
1964
Chromatic number and topological complete subgraphs. Zbl 0141.41004
Dirac, G. A.
2
1965
Note on Hamilton circuits and Hamilton paths. Zbl 0247.05149
Dirac, G. A.
1
1973
Terminable and interminable paths and trails in infinite graphs. Zbl 0287.05110
Dirac, G. A.
1
1974
On the existence of certain subgraphs in infinite graphs. Zbl 0299.05120
Dirac, G. A.; Thomassen, C.
1
1974
Note on infinite graphs. Zbl 0321.05137
Dirac, G. A.
1
1975
On systems of paths and circuits in graphs. Zbl 0234.05113
Dirac, G. A.
1
1973
Theorems related to the four colour conjecture. Zbl 0055.17003
Dirac, G. A.
1
1954
Connectedness and structure in graphs. Zbl 0097.39101
Dirac, G. A.
1
1960
On complete graphs and complete stars contained as subgraphs in graphs. Zbl 0117.41104
Dirac, G. A.
1
1963
Hamilton circuits and long circuits. Zbl 0376.05035
Dirac, G. A.
4
1978
Structural properties and circuits in graphs. Zbl 0322.05131
Dirac, G. A.
3
1976
Note on infinite graphs. Zbl 0321.05137
Dirac, G. A.
1
1975
The number of edges in critical graphs. Zbl 0298.05119
Dirac, G. A.
14
1974
An extremal result for graphs with an application to their colourings. Zbl 0298.05117
Dirac, G. A.; Sorensen, B. Aagaard; Toft, B.
2
1974
Terminable and interminable paths and trails in infinite graphs. Zbl 0287.05110
Dirac, G. A.
1
1974
On the existence of certain subgraphs in infinite graphs. Zbl 0299.05120
Dirac, G. A.; Thomassen, C.
1
1974
Graphs in which every finite path is contained in a circuit. Zbl 0239.05129
Dirac, G. A.; Thomassen, C.
11
1973
On separating sets and Menger’s theorem. Zbl 0251.05124
Dirac, Gabriel
3
1973
On arbitrarily traceable graphs. Zbl 0259.05119
Dirac, Gabriel
3
1973
Note on Hamilton circuits and Hamilton paths. Zbl 0247.05149
Dirac, G. A.
1
1973
On systems of paths and circuits in graphs. Zbl 0234.05113
Dirac, G. A.
1
1973
On Hamilton circuits and Hamilton paths. Zbl 0222.05114
Dirac, G. A.
6
1972
Minimally 2-connected graphs. Zbl 0153.25804
Dirac, G. A.
61
1967
On the structure of k-chromatic graphs. Zbl 0161.20704
Dirac, G. A.
9
1967
Short proof of Menger’s graph theorem. Zbl 0144.45102
Dirac, G. A.
9
1966
Chromatic number and topological complete subgraphs. Zbl 0141.41004
Dirac, G. A.
2
1965
On the structure of 5- and 6-chromatic abstract graphs. Zbl 0131.38403
Dirac, G. A.
22
1964
Graph union and chromatic number. Zbl 0126.39303
Dirac, G. A.
2
1964
Homomorphism theorems for graphs. Zbl 0115.41005
Dirac, G. A.
32
1963
Some results concerning the structure of graphs. Zbl 0138.19203
Dirac, G. A.
32
1963
Extensions of Menger’s theorem. Zbl 0112.38606
Dirac, G. A.
18
1963
On the maximal number of independent circuits in a graph. Zbl 0122.24903
Dirac, G.; Erdős, Pál
14
1963
Extensions of Turan’s theorem on graphs. Zbl 0113.24703
Dirac, G.
11
1963
On the maximal number of independent triangles in graphs. Zbl 0111.35901
Dirac, G. A.
9
1963
On the four-colour conjecture. Zbl 0112.15002
Dirac, G. A.
5
1963
Percy John Heawood (1861-1955). Zbl 0112.00305
Dirac, G. A.
2
1963
On complete graphs and complete stars contained as subgraphs in graphs. Zbl 0117.41104
Dirac, G. A.
1
1963
On rigid circuit graphs. Zbl 0098.14703
Dirac, G. A.
377
1961
A contraction theorem for abstract graphs. Zbl 0107.17301
Dirac, G. A.
3
1961
Corrigendum. A theorem of Kuratowski. Zbl 0098.36606
Dirac, G. A.; Schuster, S.
2
1961
In abstrakten Graphen vorhandene vollständige 4-Graphen und ihre Unterteilungen. Zbl 0096.17903
Dirac, Gabriel Andrew
102
1960
4-chrome Graphen und vollständige 4-Graphen. Zbl 0096.17902
Dirac, Gabriel Andrew
13
1960
Trennende Knotenpunktmengen und Reduzibilität abstrakter Graphen mit Anwendung auf das Vierfarbenproblem. Zbl 0096.17901
Dirac, G. A.
10
1960
Généralisations du théorème de Menger. Zbl 0095.37803
Dirac, Gábor
7
1960
Connectedness and structure in graphs. Zbl 0097.39101
Dirac, G. A.
1
1960
Paths and circuits in graphs: Extreme cases. Zbl 0090.39305
Dirac, G. A.
3
1959
A theorem of R. L. Brooks and a conjecture of H. Hadwiger. Zbl 0077.17002
Dirac, G. A.
43
1957
Short proof of a map-colour theorem. Zbl 0077.36802
Dirac, G. A.
11
1957
Map colour theorems related to the Heawood colour formula. II. Zbl 0078.16503
Dirac, G. A.
3
1957
Map colour theorems related to the Heawood colour formula. Zbl 0071.17701
Dirac, G. A.
12
1956
Circuits in critical graphs. Zbl 0065.39001
Dirac, G. A.
4
1955
A theorem of Kuratowski. Zbl 0055.17002
Dirac, G. A.; Schuster, S.
25
1954
Theorems related to the four colour conjecture. Zbl 0055.17003
Dirac, G. A.
1
1954
The structure of \(k\)-chromatic graphs. Zbl 0053.13102
Dirac, G. A.
29
1953
The colouring of maps. Zbl 0051.14702
Dirac, G. A.
6
1953
Some theorems on abstract graphs. Zbl 0047.17001
Dirac, G. A.
612
1952
A property of 4-chromatic graphs and some remarks on critical graphs. Zbl 0046.41001
Dirac, G. A.
147
1952
Map-colour theorems. Zbl 0047.42203
Dirac, G. A.
26
1952
Ovals with equichordal points. Zbl 0047.15804
Dirac, G. A.
2
1952
Collinearity properties of sets of points. Zbl 0043.14602
Dirac, G. A.
24
1951
Note on the colouring of graphs. Zbl 0043.38502
Dirac, G. A.
17
1951
Note on a problem in additive number theory. Zbl 0043.04702
Dirac, G. A.
8
1951
all top 5

Cited by 1,840 Authors

28 Kostochka, Aleksandr Vasil’evich
24 Thomassen, Carsten
22 Faudree, Ralph Jasper jun.
22 Li, Hao
20 Gould, Ronald J.
20 Kawarabayashi, Ken-ichi
20 Li, Binlong
19 Jacobson, Michael Scott
16 Chen, Yaojun
16 Stiebitz, Michael
14 Broersma, Hajo J.
14 Sudakov, Benny
13 Bauer, Douglas
12 Hoàng, Chính T.
12 Schiermeyer, Ingo
11 Chen, Guantao
11 Dirac, Gabriel Andrew
11 Kierstead, Henry A.
11 Oxley, James G.
11 Tuza, Zsolt
11 Wood, David Ronald
10 Berry, Anne
10 Böttcher, Julia
10 Erdős, Pál
10 Halin, Rudolf
10 Heggernes, Pinar
10 Lesniak, Linda M.
10 Maffray, Frédéric
10 Ning, Bo
10 Rodl, Vojtech
10 Schmeichel, Edward F.
10 Seymour, Paul D.
10 Xiong, Liming
9 Krivelevich, Michael
9 Mycroft, Richard
9 Oellermann, Ortrud R.
8 Lai, Hong-Jian
8 Ma, Jie
8 Mader, Wolfgang
8 Milanič, Martin
8 Saito, Akira
8 Taraz, Anusch
8 Thomas, Robin
8 Yamashita, Tomoki
8 Yu, Xingxing
8 Zhang, Shenggui
8 Zhang, Yunqing
8 Zhao, Yi
7 Asratian, Armen S.
7 Cai, Junqing
7 Ferrara, Michael J.
7 Gutierrez, Marisa
7 Herzog, Jürgen
7 Jackson, Bill
7 Kühn, Daniela
7 Locke, Stephen C.
7 Magnant, Colton
7 Osthus, Deryk
7 Plummer, Michael D.
7 Robertson, Neil
7 Schacht, Mathias
7 Song, Zixia
7 Sritharan, R.
7 Toft, Bjarne
7 Veldman, Henk Jan
7 Vušković, Kristina
7 Yan, Jin
7 Yu, Gexin
6 Albertson, Michael O.
6 Chang, Gerard Jennhwa
6 Dahlhaus, Elias
6 Debiasio, Louis
6 Fomin, Fedor V.
6 Furedi, Zoltan
6 Golovach, Petr A.
6 Győri, Ervin
6 Han, Jie
6 Harant, Jochen
6 Hibi, Takayuki
6 Hsu, Lihhsing
6 Hutchinson, Joan P.
6 Lemos, Manoel José Machado Soares
6 Mafuta, Phillip
6 Mohar, Bojan
6 Postle, Luke
6 Ruciński, Andrzej
6 Sarkozy, Gabor N.
6 Schelp, Richard Herbert
6 Szemerédi, Endre
6 Thomason, Andrew G.
6 Trotignon, Nicolas
6 West, Douglas Brent
6 Woodall, Douglas R.
6 Zhang, Cunquan
5 Abbott, Harvey Leslie
5 Aboulker, Pierre
5 Balogh, József
5 Bang-Jensen, Jørgen
5 Bodlaender, Hans L.
5 Bollobás, Béla
...and 1,740 more Authors
all top 5

Cited in 193 Serials

331 Discrete Mathematics
160 Journal of Combinatorial Theory. Series B
126 Discrete Applied Mathematics
93 Graphs and Combinatorics
59 Journal of Graph Theory
48 Combinatorica
48 The Electronic Journal of Combinatorics
47 European Journal of Combinatorics
35 SIAM Journal on Discrete Mathematics
33 Theoretical Computer Science
25 Information Processing Letters
22 Journal of Combinatorial Theory. Series A
21 Mathematische Annalen
18 Combinatorics, Probability and Computing
14 Linear Algebra and its Applications
12 Random Structures & Algorithms
11 Algorithmica
11 Discussiones Mathematicae. Graph Theory
11 Journal of Combinatorial Optimization
9 Applied Mathematics and Computation
9 Discrete & Computational Geometry
8 Archiv der Mathematik
8 Transactions of the American Mathematical Society
8 Annals of Combinatorics
8 Acta Mathematica Sinica. English Series
7 Acta Mathematica Academiae Scientiarum Hungaricae
7 Israel Journal of Mathematics
7 Periodica Mathematica Hungarica
7 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
7 Journal of Algebra
7 Monatshefte für Mathematik
6 Journal of Computer and System Sciences
6 Proceedings of the American Mathematical Society
6 Applied Mathematics Letters
6 International Journal of Computer Mathematics
5 Communications in Algebra
5 Journal of Mathematical Analysis and Applications
5 Czechoslovak Mathematical Journal
5 Mathematica Slovaca
5 SIAM Journal on Algebraic and Discrete Methods
5 Acta Mathematicae Applicatae Sinica. English Series
5 Journal of Algebraic Combinatorics
4 Linear and Multilinear Algebra
4 Advances in Applied Mathematics
4 Aequationes Mathematicae
4 European Journal of Operational Research
4 Journal of Mathematical Sciences (New York)
4 Ars Mathematica Contemporanea
4 Discrete Mathematics, Algorithms and Applications
4 Algorithms
4 Electronic Journal of Graph Theory and Applications
3 Communications in Mathematical Physics
3 Advances in Mathematics
3 International Journal of Mathematics and Mathematical Sciences
3 Networks
3 Quaestiones Mathematicae
3 Acta Mathematica Hungarica
3 Computational Geometry
3 Mathematical Programming. Series A. Series B
3 The Australasian Journal of Combinatorics
3 Journal of Discrete Mathematical Sciences & Cryptography
3 Journal of Applied Mathematics and Computing
3 Foundations of Physics
3 Discrete Optimization
3 Applicable Analysis and Discrete Mathematics
3 Journal of Commutative Algebra
2 Computers & Mathematics with Applications
2 General Relativity and Gravitation
2 Indian Journal of Pure & Applied Mathematics
2 International Journal of Theoretical Physics
2 Mathematical Notes
2 Mathematical Proceedings of the Cambridge Philosophical Society
2 Annali di Matematica Pura ed Applicata. Serie Quarta
2 BIT
2 Geometriae Dedicata
2 Journal of Geometry
2 Journal of Pure and Applied Algebra
2 Journal of Soviet Mathematics
2 Journal of Statistical Planning and Inference
2 Manuscripta Mathematica
2 Mathematische Nachrichten
2 Rendiconti del Seminario Matemàtico e Fisico di Milano
2 Order
2 Information and Computation
2 Proceedings of the Indian Academy of Sciences. Mathematical Sciences
2 Journal of the European Mathematical Society (JEMS)
2 Journal of Algebra and its Applications
2 Journal of Discrete Algorithms
2 AKCE International Journal of Graphs and Combinatorics
2 Mathematics in Computer Science
2 Groups, Geometry, and Dynamics
2 Forum of Mathematics, Sigma
2 Open Mathematics
2 Prikladnaya Diskretnaya Matematika
1 Artificial Intelligence
1 Educational Studies in Mathematics
1 Journal of the Franklin Institute
1 Journal of Statistical Physics
1 Rocky Mountain Journal of Mathematics
1 Theoretical and Mathematical Physics
...and 93 more Serials
all top 5

Cited in 39 Fields

1,414 Combinatorics (05-XX)
171 Computer science (68-XX)
42 Commutative algebra (13-XX)
41 Convex and discrete geometry (52-XX)
40 Operations research, mathematical programming (90-XX)
21 Manifolds and cell complexes (57-XX)
19 Group theory and generalizations (20-XX)
15 Linear and multilinear algebra; matrix theory (15-XX)
15 Geometry (51-XX)
13 Number theory (11-XX)
13 Statistics (62-XX)
12 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
10 Numerical analysis (65-XX)
10 Quantum theory (81-XX)
9 Order, lattices, ordered algebraic structures (06-XX)
9 Biology and other natural sciences (92-XX)
8 Algebraic geometry (14-XX)
7 Mathematical logic and foundations (03-XX)
5 Associative rings and algebras (16-XX)
5 Probability theory and stochastic processes (60-XX)
5 Information and communication theory, circuits (94-XX)
4 Several complex variables and analytic spaces (32-XX)
3 General and overarching topics; collections (00-XX)
3 Differential geometry (53-XX)
3 General topology (54-XX)
3 Optics, electromagnetic theory (78-XX)
3 Relativity and gravitational theory (83-XX)
2 History and biography (01-XX)
2 Nonassociative rings and algebras (17-XX)
2 Real functions (26-XX)
2 Functions of a complex variable (30-XX)
2 Statistical mechanics, structure of matter (82-XX)
1 Partial differential equations (35-XX)
1 Dynamical systems and ergodic theory (37-XX)
1 Operator theory (47-XX)
1 Algebraic topology (55-XX)
1 Global analysis, analysis on manifolds (58-XX)
1 Mechanics of particles and systems (70-XX)
1 Mathematics education (97-XX)

Citations by Year

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