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

Authors :
Christofides, Demetres
Edwards, Katherine
King, Andrew D.
Publication Year :
2011

Abstract

It was recently proved that any graph satisfying $\omega > \frac 23(\Delta+1)$ contains a stable set hitting every maximum clique. In this note we prove that the same is true for graphs satisfying $\omega \geq \frac 23(\Delta+1)$ unless the graph is the strong product of $K_{\omega/2}$ and an odd hole. We also provide a counterexample to a recent conjecture on the existence of a stable set hitting every sufficiently large maximal clique.<br />Comment: 7 pages, two figures, accepted to J. Graph Theory

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.1109.3092
Document Type :
Working Paper