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CLIQUE-TRANSVERSAL SETS IN LINE GRAPHS OF CUBIC GRAPHS AND TRIANGLE-FREE GRAPHS

  • KANG, LIYING ;
  • SHAN, ERFANG
  • Received : 2013.11.06
  • Published : 2015.09.30

Abstract

A clique-transversal set D of a graph G is a set of vertices of G such that D meets all cliques of G. The 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

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Acknowledgement

Supported by : National Nature Science Foundation of China