Bull. Korean Math. Soc. 2015; 52(5): 1423-1431
Printed September 30, 2015
https://doi.org/10.4134/BKMS.2015.52.5.1423
Copyright © The Korean Mathematical Society.
Liying Kang and Erfang Shan
Shanghai University, Shanghai University
A {\em clique-transversal set} $D$ of a graph $G$ is a set of vertices of $G$ such that $D$ meets all cliques of $G$. The {\em clique-transversal number} is the minimum cardinality of a clique-transversal set in $G$. For every cubic graph with at most two bridges, we first show that it has a perfect matching which contains exactly one edge of each triangle of it; by the result, we determine the exact value of the clique-transversal number of line graph of it. Also, we present a sharp upper bound on the clique-transversal number of line graph of a cubic graph. Furthermore, we prove that the clique-transversal number of line graph of a triangle-free graph is at most the chromatic number of complement of the triangle-free graph.
Keywords: matching, clique-transversal set, clique-transversal number, cubic graph, line graph
MSC numbers: 05C69, 05C65, 05C15
2017; 54(1): 331-342
2002; 39(1): 175-184
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd