Maximum set of edges no two covered by a clique

Abstract

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.

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Kostochka, A.V. Maximum set of edges no two covered by a clique. Combinatorica 5, 229–235 (1985). https://doi.org/10.1007/BF02579366

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AMS subject classification (1980)

  • 05 C 35
  • 05 C 15