A note on hitting maximum and maximal cliques with a stable set

  title={A note on hitting maximum and maximal cliques with a stable set},
  author={Demetres Christofides and Katherine L Edwards and Andrew D. King},
  journal={Journal of Graph Theory},
It was recently proved that any graph satisfying ω > 2 3(∆ + 1) contains a stable set hitting every maximum clique. In this note we prove that the same is true for graphs satisfying ω ≥ 23(∆ + 1) unless the graph is the strong product of an odd hole and Kω/2. We also provide a counterexample to a recent conjecture on the existence of a stable set hitting every sufficiently large maximal clique. 

From This Paper

Figures, tables, and topics from this paper.
2 Citations
15 References
Similar Papers


Publications citing this paper.
Showing 1-2 of 2 extracted citations


Publications referenced by this paper.
Showing 1-10 of 15 references


  • A. V. Kostochka
  • density, and chromatic number of graphs. Metody…
  • 1980
Highly Influential
4 Excerpts

Kostochka . Degree , density , and chromatic number of graphs

  • V. A.
  • Metody Diskret . Analiz .
  • 2011

Claw-free graphs and two conjectures on ω, ∆, and χ

  • A. D. King
  • PhD thesis,
  • 2009
1 Excerpt


  • B. A. Reed
  • ∆, and χ. J. Graph Theory, 27:177–212
  • 1998
1 Excerpt

Similar Papers

Loading similar papers…