Gallai–Hasse–Roy–Vitaver theorem (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Gallai–Hasse–Roy–Vitaver theorem" in English language version.

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Hsu, Lih-Hsing; Lin, Cheng-Kuan (2009), "Theorem 8.5", Graph Theory and Interconnection Networks, Boca Raton, Florida: CRC Press, pp. 129–130, ISBN 978-1-4200-4481-2, MR 2454502
Nešetřil, Jaroslav; Ossona de Mendez, Patrice (2012), "Section 3.7: Homomorphisms", Sparsity: Graphs, Structures, and Algorithms, Algorithms and Combinatorics, vol. 28, Heidelberg: Springer, pp. 39–46, doi:10.1007/978-3-642-27875-4, ISBN 978-3-642-27874-7, MR 2920058; see especially Theorem 3.13, p. 42
Chartrand, Gary; Zhang, Ping (2009), "Theorem 7.17 (The Gallai–Roy–Vitaver Theorem)", Chromatic Graph Theory, Discrete Mathematics and its Applications, Boca Raton, Florida: CRC Press, ISBN 978-1-58488-800-0, MR 2450569
Li, Hao (2001), "A generalization of the Gallai–Roy theorem", Graphs and Combinatorics, 17 (4): 681–685, doi:10.1007/PL00007256, MR 1876576, S2CID 37646065
Chang, Gerard J.; Tong, Li-Da; Yan, Jing-Ho; Yeh, Hong-Gwa (2002), "A note on the Gallai–Roy–Vitaver theorem", Discrete Mathematics, 256 (1–2): 441–444, doi:10.1016/S0012-365X(02)00386-2, MR 1927565
Guzmán-Pro, Santiago; Hernández-Cruz, César (2022), "Oriented expressions of graph properties", European Journal of Combinatorics, 105, Paper No. 103567, arXiv:2012.12811, doi:10.1016/j.ejc.2022.103567, MR 4432176, S2CID 229363421
Матиясевич, Ю. В. (1974), "Одна схема доказательств в дискретной математике" [A certain scheme for proofs in discrete mathematics], Исследования по конструктивной математике и математической логике [Studies in constructive mathematics and mathematical logic. Part VI. Dedicated to A. A. Markov on the occasion of his 70th birthday], Zapiski Naučnyh Seminarov Leningradskogo Otdelenija Matematičeskogo Instituta im. V. A. Steklova Akademii Nauk SSSR (LOMI) (in Russian), vol. 40, pp. 94–100, MR 0363823
Nešetřil, Jaroslav; Tardif, Claude (2008), "A dualistic approach to bounding the chromatic number of a graph", European Journal of Combinatorics, 29 (1): 254–260, doi:10.1016/j.ejc.2003.09.024, MR 2368632
Hasse, Maria (1965), "Zur algebraischen Begründung der Graphentheorie. I", Mathematische Nachrichten (in German), 28 (5–6): 275–290, doi:10.1002/mana.19650280503, MR 0179105
Roy, B. (1967), "Nombre chromatique et plus longs chemins d'un graphe" (PDF), Rev. Française Informat. Recherche Opérationnelle (in French), 1 (5): 129–132, doi:10.1051/m2an/1967010501291, MR 0225683
Витавер, Л. М. (1962), "Нахождение минимальных раскрасок вершин графа с помощью булевых степеней матрицы смежностей [Determination of minimal coloring of vertices of a graph by means of Boolean powers of the incidence matrix]", Doklady Akademii Nauk SSSR (in Russian), 147: 758–759, MR 0145509
Gutin, G. (1994), "Minimizing and maximizing the diameter in orientations of graphs", Graphs and Combinatorics, 10 (3): 225–230, doi:10.1007/BF02986669, MR 1304376, S2CID 2453716
Bondy, J. A. (2003), "Short proofs of classical theorems", Journal of Graph Theory, 44 (3): 159–165, doi:10.1002/jgt.10135, MR 2012799, S2CID 2174153

arxiv.org

Guzmán-Pro, Santiago; Hernández-Cruz, César (2022), "Oriented expressions of graph properties", European Journal of Combinatorics, 105, Paper No. 103567, arXiv:2012.12811, doi:10.1016/j.ejc.2022.103567, MR 4432176, S2CID 229363421

books.google.com

Hsu, Lih-Hsing; Lin, Cheng-Kuan (2009), "Theorem 8.5", Graph Theory and Interconnection Networks, Boca Raton, Florida: CRC Press, pp. 129–130, ISBN 978-1-4200-4481-2, MR 2454502
Chartrand, Gary; Zhang, Ping (2009), "Theorem 7.17 (The Gallai–Roy–Vitaver Theorem)", Chromatic Graph Theory, Discrete Mathematics and its Applications, Boca Raton, Florida: CRC Press, ISBN 978-1-58488-800-0, MR 2450569

doi.org

Nešetřil, Jaroslav; Ossona de Mendez, Patrice (2012), "Section 3.7: Homomorphisms", Sparsity: Graphs, Structures, and Algorithms, Algorithms and Combinatorics, vol. 28, Heidelberg: Springer, pp. 39–46, doi:10.1007/978-3-642-27875-4, ISBN 978-3-642-27874-7, MR 2920058; see especially Theorem 3.13, p. 42
Li, Hao (2001), "A generalization of the Gallai–Roy theorem", Graphs and Combinatorics, 17 (4): 681–685, doi:10.1007/PL00007256, MR 1876576, S2CID 37646065
Chang, Gerard J.; Tong, Li-Da; Yan, Jing-Ho; Yeh, Hong-Gwa (2002), "A note on the Gallai–Roy–Vitaver theorem", Discrete Mathematics, 256 (1–2): 441–444, doi:10.1016/S0012-365X(02)00386-2, MR 1927565
Guzmán-Pro, Santiago; Hernández-Cruz, César (2022), "Oriented expressions of graph properties", European Journal of Combinatorics, 105, Paper No. 103567, arXiv:2012.12811, doi:10.1016/j.ejc.2022.103567, MR 4432176, S2CID 229363421
Mirsky, Leon (1971), "A dual of Dilworth's decomposition theorem", American Mathematical Monthly, 78 (8): 876–877, doi:10.2307/2316481, JSTOR 2316481
Nešetřil, Jaroslav; Tardif, Claude (2008), "A dualistic approach to bounding the chromatic number of a graph", European Journal of Combinatorics, 29 (1): 254–260, doi:10.1016/j.ejc.2003.09.024, MR 2368632
Hasse, Maria (1965), "Zur algebraischen Begründung der Graphentheorie. I", Mathematische Nachrichten (in German), 28 (5–6): 275–290, doi:10.1002/mana.19650280503, MR 0179105
Roy, B. (1967), "Nombre chromatique et plus longs chemins d'un graphe" (PDF), Rev. Française Informat. Recherche Opérationnelle (in French), 1 (5): 129–132, doi:10.1051/m2an/1967010501291, MR 0225683
Gutin, G. (1994), "Minimizing and maximizing the diameter in orientations of graphs", Graphs and Combinatorics, 10 (3): 225–230, doi:10.1007/BF02986669, MR 1304376, S2CID 2453716
Bondy, J. A. (2003), "Short proofs of classical theorems", Journal of Graph Theory, 44 (3): 159–165, doi:10.1002/jgt.10135, MR 2012799, S2CID 2174153

grenoble-inp.fr

oc.g-scop.grenoble-inp.fr

Havet, Frédéric (2013), "Section 3.1: Gallai–Roy Theorem and related results", Orientations and colouring of graphs (PDF), Lecture notes for the summer school SGT 2013 in Oléron, France, pp. 15–19

jstor.org

Mirsky, Leon (1971), "A dual of Dilworth's decomposition theorem", American Mathematical Monthly, 78 (8): 876–877, doi:10.2307/2316481, JSTOR 2316481

mathnet.ru

Матиясевич, Ю. В. (1974), "Одна схема доказательств в дискретной математике" [A certain scheme for proofs in discrete mathematics], Исследования по конструктивной математике и математической логике [Studies in constructive mathematics and mathematical logic. Part VI. Dedicated to A. A. Markov on the occasion of his 70th birthday], Zapiski Naučnyh Seminarov Leningradskogo Otdelenija Matematičeskogo Instituta im. V. A. Steklova Akademii Nauk SSSR (LOMI) (in Russian), vol. 40, pp. 94–100, MR 0363823

numdam.org

archive.numdam.org

Roy, B. (1967), "Nombre chromatique et plus longs chemins d'un graphe" (PDF), Rev. Française Informat. Recherche Opérationnelle (in French), 1 (5): 129–132, doi:10.1051/m2an/1967010501291, MR 0225683

semanticscholar.org

api.semanticscholar.org

Li, Hao (2001), "A generalization of the Gallai–Roy theorem", Graphs and Combinatorics, 17 (4): 681–685, doi:10.1007/PL00007256, MR 1876576, S2CID 37646065
Guzmán-Pro, Santiago; Hernández-Cruz, César (2022), "Oriented expressions of graph properties", European Journal of Combinatorics, 105, Paper No. 103567, arXiv:2012.12811, doi:10.1016/j.ejc.2022.103567, MR 4432176, S2CID 229363421
Gutin, G. (1994), "Minimizing and maximizing the diameter in orientations of graphs", Graphs and Combinatorics, 10 (3): 225–230, doi:10.1007/BF02986669, MR 1304376, S2CID 2453716
Bondy, J. A. (2003), "Short proofs of classical theorems", Journal of Graph Theory, 44 (3): 159–165, doi:10.1002/jgt.10135, MR 2012799, S2CID 2174153