On the chromatic number of graphs with some restriction of vertex degrees

S.N. Selezneva

Lomonosov Moscow State University, Moscow, 119991 Russia

E-mail: selezn@cs.msu.ru

Received October 23, 2020

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DOI: 10.26907/2541-7746.2020.4.387-395

For citation: Selezneva S.N. On the chromatic number of graphs with some restriction of vertex degrees. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2020, vol. 162, no. 4, pp. 387–395. doi: 10.26907/2541-7746.2020.4.387-395. (In Russian)

Abstract

Graphs, for which the degree of a certain vertex is equal to (d + 1) and the degrees of all other vertices are at most d , d ≥ 3 , were considered. Properties were obtained to color vertices of these graphs in d colors.

Keywords: graph, coloring, vertex coloring, chromatic number, degree of vertex in graph

Acknowledgments. The study was supported by the Moscow Center for Fundamental and Applied Mathematics, Moscow State University (project “Bounds for complexity characteristics of Boolean functions and graphs”, 2020).

References

  1. Emelichev V.A., Mel’nikov O.I., Sarvanov V.I., Tyshkevich R.I. Lektsii po teorii grafov [Lectures on Graph Theory]. Moscow, Librokom, 2009. 383 p. (In Russian)
  2. Bondy J.A., Murty U.S.R. Graph Theory. Springer, 2008. 655 p.
  3. Stockmeyer L.J. Planar 3 -colorability is NP -complete. SIGACT News, 1973, vol. 5, no. 3, pp. 19–25.
  4. Garey M.R., Johnson D.S., Stockmeyer L. Some simplified NP -complete graph problems. Theor. Comput. Sci., 1976, vol. 1, no. 3, pp. 237–267. doi: 10.1016/0304-3975(76)90059-1.
  5. Malyshev D.S. A complete classification of the complexity of the vertex 3-colourability problem for quadruples of induced 5 -vertex prohibitions. Zh. Srednevolzh. Mat. O-va., 2020, vol. 22, no. 1, pp. 38–47. doi: 10.15507/2079-6900.22.202001.38-47. (In Russian)
  6. Selezneva S.N., Mel’nik M.V., Astakhova A.V. Coloring of pseudocubic graphs in three colors. Moscow Univ. Comput. Math. Cybern., 2019, vol. 43, no. 2, pp. 82–88. doi: 10.3103/S0278641919020079.
  7. Vizing V.G. Coloring graph vertices in prescribed colors. In: Metody diskretnogo analiza v teorii kodov i skhem: Sb. nauch. tr. [Discrete Analysis Methods in the Theory of Codes and Schemes: A Collection of Papers]. Novosibirsk, Inst. Mat. Sib. Otd. SSSR, 1976, no. 29, pp. 3–10. (In Russian)

 

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