대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제52권5호
  • /
  • Pages.1423-1431
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  • 2015
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  • 1015-8634(pISSN)
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  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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CLIQUE-TRANSVERSAL SETS IN LINE GRAPHS OF CUBIC GRAPHS AND TRIANGLE-FREE GRAPHS

  • KANG, LIYING (DEPARTMENT OF MATHEMATICS SHANGHAI UNIVERSITY) ;
  • SHAN, ERFANG (DEPARTMENT OF MATHEMATICS SHANGHAI UNIVERSITY, SCHOOL OF MANAGEMENT SHANGHAI UNIVERSITY)
  • 투고 : 2013.11.06
  • 발행 : 2015.09.30
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초록

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.

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참고문헌

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