Journal of Mathematical Sciences

, Volume 179, Issue 5, pp 579–591 | Cite as

Chromatic numbers of layered graphs with a bounded maximal clique

  • S. L. Berlov

A graph is called n-layered if the set of its vertices is a union of pairwise nonintersecting n-cliques. We estimatechromatic numbers of n-layered graphs without (n + 1)-cliques. Bibliography: 10 titles.


Russia High School Layered Graph Chromatic Number Maximal Clique 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    R. L. Brooks, “On coloring the nodes of a network,” Proc. Cambrige Phil. Soc., 37, 194–197 (1941).CrossRefMathSciNetGoogle Scholar
  2. 2.
    B. Reed, “A strengthening of Brooks’ theorem,” J.Combin. Theory, Ser. B, 76, 136–149 (1999).CrossRefMATHMathSciNetGoogle Scholar
  3. 3.
    A. V. Kostochka, “Degree, density, and chromatic number of graphs,” Metody Diskret. Analiza, 35, 45–70; 104–105 (1980).MATHMathSciNetGoogle Scholar
  4. 4.
    N. Alon, “The strong chromatic number of a graph,” Random Struct. Alg., 3, 1–7 (1992).CrossRefMATHGoogle Scholar
  5. 5.
    P. E. Haxell, “On the strong chromatic number,” Combin., Probab. Comput., 13, 857–865 (2004).CrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    V. L. Dol’nikov, “On one coloring problem,” Sib. Mat. Zh., 13, 1272–1281 (1972).MATHMathSciNetGoogle Scholar
  7. 7.
    P. Erdös, “Some remarks on the theory of graphs,” Bull. Amer. Math. Soc., 53, 292–294 (1947).CrossRefMATHMathSciNetGoogle Scholar
  8. 8.
    R. L. Graham, B. L. Rothschild, and J. H. Spencer. Ramsey Theory, 2nd ed, John Wiley and Sons, Inc. (1990)Google Scholar
  9. 9.
    E. A. Nordhaus, “On the density and chromatic number of graphs,” Lect. Notes Math., 110, 245–249 (1969).CrossRefMathSciNetGoogle Scholar
  10. 10.
    K. Schurger, “Inequalities for the chromatic number of graphs,” J. Combin. Theory, Ser. B, 16, 77–85 (1974).CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2011

Authors and Affiliations

  1. 1.High School No. 239St.PetersburgRussia

Personalised recommendations