Maximum set of edges no two covered by a clique


Leth(G) be the largest number of edges of the graphG. no two of which are contained in the same clique. ForG without isolated vertices it is proved that ifh(G)≦5, thenχ(\(\bar G\))≦h(G), but ifh(G)=6 thenχ(\(\bar G\)) can be arbitrarily large.

This is a preview of subscription content, access via your institution.


  1. [1]

    R. C. Brigham andR. D. Dutton, On clique covers and independence numbers of graphs,Discrete Math.,44 (1983), 139–144.

    MATH  Article  MathSciNet  Google Scholar 

  2. [2]

    P. Erdős, On the covering of the vertices of a graph by cliques,J. Math. Res. Exposition,2 (1982), 93–96.

    Google Scholar 

  3. [3]

    P. Erdős, A. W. Goodman andL. Pósa. The representations of a graph by set intersections,Canad. J. Math.,18 (1966), 106–112.

    MathSciNet  Google Scholar 

  4. [4]

    P. Erdős andJ. Spencer,Probabilistic methods in combinatorics, Akadémiai Kiadó, Budapest, 1974, (Theorem 11.2).

    Google Scholar 

  5. [5]

    J. Orlin, Contentement in Graph Theory,K. Nederl. Akad. Wetensch. Proc. (Ser. A),80 (1977), 406–424.

    MathSciNet  Google Scholar 

  6. [6]

    K. R. Parthasaraty andS. A. Choudum, The edges clique cover number of products of graphs,Journ. Math. Phys. Sci.,10 (1976), 3, 255–261

    Google Scholar 

Download references

Author information



Rights and permissions

Reprints and Permissions

About this article

Cite this article

Kostochka, A.V. Maximum set of edges no two covered by a clique. Combinatorica 5, 229–235 (1985).

Download citation

AMS subject classification (1980)

  • 05 C 35
  • 05 C 15