摘要
A clique-transversal set D of a graph C is a set of vertices of G such that D meets all cliques of G. The clique-transversal number, denoted by To（G）, is the minimum cardinality of a clique- transversal set in G. In this paper we give the exact value of the clique-transversal number for the line graph of a complete graph. Also, we give a lower bound on the clique-transversal number for 4-regular claw-free graphs and characterize the extremal graphs achieving the lower bound.
A clique-transversal set D of a graph C is a set of vertices of G such that D meets all cliques of G. The clique-transversal number, denoted by To（G）, is the minimum cardinality of a clique- transversal set in G. In this paper we give the exact value of the clique-transversal number for the line graph of a complete graph. Also, we give a lower bound on the clique-transversal number for 4-regular claw-free graphs and characterize the extremal graphs achieving the lower bound.
基金
Supported by National Natural Science Foundation of China （Grant No. 60773078）, the PuJiang Project of Shanghai （Grant No. 09PJ1405000） and Key Disciplines of Shanghai Municipality （Grant No. $30104）
