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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.; Dirac, G. A.; Dirac, Gabriel; Dirac, Gabriel Andrew; Dirac, Gábor
External Links: MGP · Wikidata · GND
Documents Indexed: 68 Publications since 1951, including 3 Books
Biographic References: 4 Publications

Publications by Year

Citations contained in zbMATH Open

55 Publications have been cited 1,605 times in 1,414 Documents Cited by Year
Some theorems on abstract graphs. Zbl 0047.17001
Dirac, G. A.
526
1952
On rigid circuit graphs. Zbl 0098.14703
Dirac, G. A.
348
1961
A property of 4-chromatic graphs and some remarks on critical graphs. Zbl 0046.41001
Dirac, G. A.
133
1952
In abstrakten Graphen vorhandene vollständige 4-Graphen und ihre Unterteilungen. Zbl 0096.17903
Dirac, Gabriel Andrew
92
1960
Minimally 2-connected graphs. Zbl 0153.25804
Dirac, G. A.
56
1967
A theorem of R. L. Brooks and a conjecture of H. Hadwiger. Zbl 0077.17002
Dirac, G. A.
41
1957
Some results concerning the structure of graphs. Zbl 0138.19203
Dirac, G. A.
31
1963
Homomorphism theorems for graphs. Zbl 0115.41005
Dirac, G. A.
31
1963
On the structure of k-chromatic graphs. Zbl 0161.20704
Dirac, G. A.
25
1967
The structure of \(k\)-chromatic graphs. Zbl 0053.13102
Dirac, G. A.
23
1953
Map-colour theorems. Zbl 0047.42203
Dirac, G. A.
23
1952
A theorem of Kuratowski. Zbl 0055.17002
Dirac, G. A.; Schuster, S.
21
1954
On the structure of 5- and 6-chromatic abstract graphs. Zbl 0131.38403
Dirac, G. A.
20
1964
Collinearity properties of sets of points. Zbl 0043.14602
Dirac, G. A.
20
1951
Extensions of Menger’s theorem. Zbl 0112.38606
Dirac, G. A.
18
1963
The number of edges in critical graphs. Zbl 0298.05119
Dirac, G. A.
15
1974
4-chrome Graphen und vollständige 4-Graphen. Zbl 0096.17902
Dirac, Gabriel Andrew
13
1960
Note on the colouring of graphs. Zbl 0043.38502
Dirac, G. A.
13
1951
On the maximal number of independent circuits in a graph. Zbl 0122.24903
Dirac, G.; Erdős, Pál
11
1963
Short proof of a map-colour theorem. Zbl 0077.36802
Dirac, G. A.
11
1957
Graphs in which every finite path is contained in a circuit. Zbl 0239.05129
Dirac, G. A.; Thomassen, C.
10
1973
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
Extensions of Turan’s theorem on graphs. Zbl 0113.24703
Dirac, G.
9
1963
Map colour theorems related to the Heawood colour formula. Zbl 0071.17701
Dirac, G. A.
9
1956
On the maximal number of independent triangles in graphs. Zbl 0111.35901
Dirac, G. A.
7
1963
Généralisations du théorème de Menger. Zbl 0095.37803
Dirac, Gábor
7
1960
Note on a problem in additive number theory. Zbl 0043.04702
Dirac, G. A.
7
1951
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
Simplicial decompositions of infinite graphs. Zbl 0614.05045
Dirac, Gabriel Andrew
3
1986
Structural properties and circuits in graphs. Zbl 0322.05131
Dirac, G. A.
3
1976
On arbitrarily traceable graphs. Zbl 0259.05119
Dirac, Gabriel
3
1973
On separating sets and Menger’s theorem. Zbl 0251.05124
Dirac, Gabriel
3
1973
A contraction theorem for abstract graphs. Zbl 0107.17301
Dirac, G. A.
3
1961
Paths and circuits in graphs: Extreme cases. Zbl 0090.39305
Dirac, G. A.
3
1959
Circuits in critical graphs. Zbl 0065.39001
Dirac, G. A.
3
1955
On the existence of certain subgraphs in infinite graphs. Zbl 0299.05120
Dirac, G. A.; Thomassen, C.
2
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
Graph union and chromatic number. Zbl 0126.39303
Dirac, G. A.
2
1964
Percy John Heawood (1861-1955). Zbl 0112.00305
Dirac, G. A.
2
1963
Corrigendum. A theorem of Kuratowski. Zbl 0098.36606
Dirac, G. A.; Schuster, S.
2
1961
Map colour theorems related to the Heawood colour formula. II. Zbl 0078.16503
Dirac, G. A.
2
1957
Theorems related to the four colour conjecture. Zbl 0055.17003
Dirac, G. A.
2
1954
Oals with equichordal points. Zbl 0047.15804
Dirac, G. A.
2
1952
Cardinal-determining subgraphs of infinite graphs. Zbl 0339.05118
Dirac, Gabriel
1
1977
Note on infinite graphs. Zbl 0321.05137
Dirac, G. A.
1
1975
Terminable and interminable paths and trails in infinite graphs. Zbl 0287.05110
Dirac, G. A.
1
1974
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
Chromatic number and topological complete subgraphs. Zbl 0141.41004
Dirac, G. A.
1
1965
On complete graphs and complete stars contained as subgraphs in graphs. Zbl 0117.41104
Dirac, G. A.
1
1963
Connectedness and structure in graphs. Zbl 0097.39101
Dirac, G. A.
1
1960
Simplicial decompositions of infinite graphs. Zbl 0614.05045
Dirac, Gabriel Andrew
3
1986
Hamilton circuits and long circuits. Zbl 0376.05035
Dirac, G. A.
4
1978
Cardinal-determining subgraphs of infinite graphs. Zbl 0339.05118
Dirac, Gabriel
1
1977
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.
15
1974
On the existence of certain subgraphs in infinite graphs. Zbl 0299.05120
Dirac, G. A.; Thomassen, C.
2
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
Graphs in which every finite path is contained in a circuit. Zbl 0239.05129
Dirac, G. A.; Thomassen, C.
10
1973
On arbitrarily traceable graphs. Zbl 0259.05119
Dirac, Gabriel
3
1973
On separating sets and Menger’s theorem. Zbl 0251.05124
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.
56
1967
On the structure of k-chromatic graphs. Zbl 0161.20704
Dirac, G. A.
25
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.
1
1965
On the structure of 5- and 6-chromatic abstract graphs. Zbl 0131.38403
Dirac, G. A.
20
1964
Graph union and chromatic number. Zbl 0126.39303
Dirac, G. A.
2
1964
Some results concerning the structure of graphs. Zbl 0138.19203
Dirac, G. A.
31
1963
Homomorphism theorems for graphs. Zbl 0115.41005
Dirac, G. A.
31
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
11
1963
Extensions of Turan’s theorem on graphs. Zbl 0113.24703
Dirac, G.
9
1963
On the maximal number of independent triangles in graphs. Zbl 0111.35901
Dirac, G. A.
7
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.
348
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
92
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.
41
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.
2
1957
Map colour theorems related to the Heawood colour formula. Zbl 0071.17701
Dirac, G. A.
9
1956
Circuits in critical graphs. Zbl 0065.39001
Dirac, G. A.
3
1955
A theorem of Kuratowski. Zbl 0055.17002
Dirac, G. A.; Schuster, S.
21
1954
Theorems related to the four colour conjecture. Zbl 0055.17003
Dirac, G. A.
2
1954
The structure of \(k\)-chromatic graphs. Zbl 0053.13102
Dirac, G. A.
23
1953
The colouring of maps. Zbl 0051.14702
Dirac, G. A.
6
1953
Some theorems on abstract graphs. Zbl 0047.17001
Dirac, G. A.
526
1952
A property of 4-chromatic graphs and some remarks on critical graphs. Zbl 0046.41001
Dirac, G. A.
133
1952
Map-colour theorems. Zbl 0047.42203
Dirac, G. A.
23
1952
Oals with equichordal points. Zbl 0047.15804
Dirac, G. A.
2
1952
Collinearity properties of sets of points. Zbl 0043.14602
Dirac, G. A.
20
1951
Note on the colouring of graphs. Zbl 0043.38502
Dirac, G. A.
13
1951
Note on a problem in additive number theory. Zbl 0043.04702
Dirac, G. A.
7
1951
all top 5

Cited by 1,681 Authors

28 Kostochka, Aleksandr Vasil’evich
23 Thomassen, Carsten
22 Faudree, Ralph Jasper jun.
22 Li, Hao
19 Gould, Ronald J.
19 Jacobson, Michael Scott
19 Kawarabayashi, Ken-ichi
15 Stiebitz, Michael
14 Li, Binlong
13 Broersma, Hajo J.
12 Bauer, Douglas
12 Chen, Yaojun
12 Hoàng, Chính T.
12 Sudakov, Benny
11 Chen, Guantao
11 Dirac, Gabriel Andrew
11 Kierstead, Henry A.
11 Oxley, James G.
11 Schiermeyer, Ingo
11 Tuza, Zsolt
10 Berry, Anne
10 Böttcher, Julia
10 Erdős, Pál
10 Halin, Rudolf
10 Heggernes, Pinar
10 Maffray, Frédéric
9 Mycroft, Richard
9 Schmeichel, Edward F.
9 Seymour, Paul D.
8 Chvátal, Vašek
8 Krivelevich, Michael
8 Lesniak, Linda M.
8 Mader, Wolfgang
8 Ning, Bo
8 Oellermann, Ortrud R.
8 Rodl, Vojtech
8 Saito, Akira
8 Taraz, Anusch
8 Thomas, Robin
8 Yamashita, Tomoki
8 Yu, Xingxing
8 Zhang, Yunqing
8 Zhao, Yi
7 Cai, Junqing
7 Herzog, Jürgen
7 Jackson, Bill
7 Kühn, Daniela
7 Lai, Hong-Jian
7 Locke, Stephen C.
7 Osthus, Deryk
7 Robertson, Neil
7 Toft, Bjarne
7 Veldman, Henk Jan
7 Yu, Gexin
7 Zhang, Shenggui
6 Albertson, Michael O.
6 Asratian, Armen S.
6 Chang, Gerard Jennhwa
6 Dahlhaus, Elias
6 Ferrara, Michael J.
6 Furedi, Zoltan
6 Gutierrez, Marisa
6 Harant, Jochen
6 Hibi, Takayuki
6 Hsu, Lihhsing
6 Hutchinson, Joan P.
6 Lemos, Manoel José Machado Soares
6 Ma, Jie
6 Magnant, Colton
6 Milanič, Martin
6 Mohar, Bojan
6 Plummer, Michael D.
6 Schelp, Richard Herbert
6 Song, Zixia
6 Sritharan, R.
6 Szemerédi, Endre
6 Thomason, Andrew G.
6 Trotignon, Nicolas
6 Vušković, Kristina
6 West, Douglas Brent
6 Wood, David Ronald
6 Woodall, Douglas R.
6 Zhang, Cunquan
5 Abbott, Harvey Leslie
5 Bang-Jensen, Jørgen
5 Bollobás, Béla
5 De Caria, Pablo
5 de Figueiredo, Celina M. Herrera
5 Diestel, Reinhard
5 Fan, Genghua
5 Farber, Martin
5 Fomin, Fedor V.
5 Hamidoune, Yahya Ould
5 Han, Jie
5 Keevash, Peter
5 Kriesell, Matthias
5 Lin, Cheng-Kuan
5 Mafuta, Phillip
5 Olariu, Stephan
5 Ozeki, Kenta
...and 1,581 more Authors
all top 5

Cited in 183 Serials

309 Discrete Mathematics
150 Journal of Combinatorial Theory. Series B
112 Discrete Applied Mathematics
80 Graphs and Combinatorics
59 Journal of Graph Theory
44 European Journal of Combinatorics
44 Combinatorica
31 Theoretical Computer Science
24 Information Processing Letters
23 SIAM Journal on Discrete Mathematics
23 The Electronic Journal of Combinatorics
22 Journal of Combinatorial Theory. Series A
21 Mathematische Annalen
14 Combinatorics, Probability and Computing
13 Linear Algebra and its Applications
12 Random Structures & Algorithms
10 Algorithmica
10 Discussiones Mathematicae. Graph Theory
9 Applied Mathematics and Computation
8 Archiv der Mathematik
8 Discrete & Computational Geometry
8 Journal of Combinatorial Optimization
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 Monatshefte für Mathematik
7 Transactions of the American Mathematical Society
7 Annals of Combinatorics
6 Journal of Mathematical Analysis and Applications
6 Journal of Algebra
6 Proceedings of the American Mathematical Society
6 Applied Mathematics Letters
6 International Journal of Computer Mathematics
6 Acta Mathematica Sinica. English Series
5 Communications in Algebra
5 Physics Letters. A
5 Journal of Computer and System Sciences
5 Mathematica Slovaca
5 SIAM Journal on Algebraic and Discrete Methods
4 Linear and Multilinear Algebra
4 Nuclear Physics. B
4 Advances in Mathematics
4 Czechoslovak Mathematical Journal
4 Acta Mathematicae Applicatae Sinica. English Series
4 Annals of Physics
4 Journal of Mathematical Sciences (New York)
4 Ars Mathematica Contemporanea
4 Discrete Mathematics, Algorithms and Applications
4 Algorithms
3 Communications in Mathematical Physics
3 International Journal of Mathematics and Mathematical Sciences
3 Networks
3 Computational Geometry
3 Aequationes Mathematicae
3 Mathematical Programming. Series A. Series B
3 Journal of Algebraic Combinatorics
3 Journal of Discrete Mathematical Sciences & Cryptography
3 Foundations of Physics
3 Discrete Optimization
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 Quaestiones Mathematicae
2 Rendiconti del Seminario Matemàtico e Fisico di Milano
2 Advances in Applied Mathematics
2 Acta Mathematica Hungarica
2 Order
2 Information and Computation
2 European Journal of Operational Research
2 Proceedings of the Indian Academy of Sciences. Mathematical Sciences
2 Journal of Applied Mathematics and Computing
2 Journal of Algebra and its Applications
2 Journal of Discrete Algorithms
2 Mathematics in Computer Science
2 Groups, Geometry, and Dynamics
2 Prikladnaya Diskretnaya Matematika
1 Artificial Intelligence
1 Educational Studies in Mathematics
1 Journal of the Franklin Institute
1 Journal of Statistical Physics
1 Physics Letters. B
1 Reports on Mathematical Physics
1 Rocky Mountain Journal of Mathematics
1 Theoretical and Mathematical Physics
1 Arkiv för Matematik
1 Bulletin of Mathematical Biology
...and 83 more Serials
all top 5

Cited in 44 Fields

1,243 Combinatorics (05-XX)
151 Computer science (68-XX)
39 Commutative algebra (13-XX)
35 Convex and discrete geometry (52-XX)
35 Operations research, mathematical programming (90-XX)
25 Quantum theory (81-XX)
17 Group theory and generalizations (20-XX)
17 Manifolds and cell complexes (57-XX)
14 Linear and multilinear algebra; matrix theory (15-XX)
13 Geometry (51-XX)
12 Number theory (11-XX)
12 Statistics (62-XX)
10 Numerical analysis (65-XX)
9 Order, lattices, ordered algebraic structures (06-XX)
9 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
9 Biology and other natural sciences (92-XX)
8 Mathematical logic and foundations (03-XX)
6 General and overarching topics; collections (00-XX)
6 Algebraic geometry (14-XX)
6 Information and communication theory, circuits (94-XX)
5 Associative rings and algebras (16-XX)
5 Several complex variables and analytic spaces (32-XX)
5 Differential geometry (53-XX)
4 Probability theory and stochastic processes (60-XX)
4 Mechanics of particles and systems (70-XX)
4 Optics, electromagnetic theory (78-XX)
4 Relativity and gravitational theory (83-XX)
3 Partial differential equations (35-XX)
2 History and biography (01-XX)
2 Real functions (26-XX)
2 Dynamical systems and ergodic theory (37-XX)
2 Abstract harmonic analysis (43-XX)
2 General topology (54-XX)
2 Global analysis, analysis on manifolds (58-XX)
2 Statistical mechanics, structure of matter (82-XX)
1 Nonassociative rings and algebras (17-XX)
1 Topological groups, Lie groups (22-XX)
1 Functions of a complex variable (30-XX)
1 Ordinary differential equations (34-XX)
1 Integral equations (45-XX)
1 Functional analysis (46-XX)
1 Operator theory (47-XX)
1 Calculus of variations and optimal control; optimization (49-XX)
1 Mathematics education (97-XX)

Citations by Year

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