Clique-transversal sets in cubic graphs

Authors:
Zuosong Liang;Erfang Shan;T. C. E. Cheng
Affiliations:
Department of Mathematics, Shanghai University, Shanghai, P. R. China;Department of Mathematics, Shanghai University, Shanghai, P. R. China and Department of Logistics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong;Department of Logistics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong
Venue:
ESCAPE'07 Proceedings of the First international conference on Combinatorics, Algorithms, Probabilistic and Experimental Methodologies
Year:
2007

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Abstract

A clique-transversal set S of a graph G is a set of vertices of G such that S meets all cliques of G. The clique-transversal number, denoted τc(G), is the minimum cardinality of a clique-transversal set in G. In this paper we present an upper bound and a lower bound on τc(G) for cubic graphs, and characterize the extremal cubic graphs achieving the lower bound. In addition, we present a sharp upper bound on τc(G) for claw-free cubic graphs.