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Clique-Transversal Sets in Cubic Graphs

  • Conference paper
Combinatorics, Algorithms, Probabilistic and Experimental Methodologies (ESCAPE 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4614))

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 τ c (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 τ c (G) for cubic graphs, and characterize the extremal cubic graphs achieving the lower bound. In addition, we present a sharp upper bound on τ c (G) for claw-free cubic graphs.

This research was partially supported by The Hong Kong Polytechnic University under grant number G-YX69, the National Nature Science Foundation of China under grant 10571117, the ShuGuang Plan of Shanghai Education Development Foundation under grant 06SG42 and the Development Foundation of Shanghai Education Committee under grant 05AZ04.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai University, Shanghai 200444, P.R. China

    Zuosong Liang & Erfang Shan

  2. Department of Logistics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

    Erfang Shan & T. C. E. Cheng

Authors
  1. Zuosong Liang
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  2. Erfang Shan
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  3. T. C. E. Cheng
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Editor information

Bo Chen Mike Paterson Guochuan Zhang

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© 2007 Springer-Verlag Berlin Heidelberg

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Liang, Z., Shan, E., Cheng, T.C.E. (2007). Clique-Transversal Sets in Cubic Graphs. In: Chen, B., Paterson, M., Zhang, G. (eds) Combinatorics, Algorithms, Probabilistic and Experimental Methodologies. ESCAPE 2007. Lecture Notes in Computer Science, vol 4614. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74450-4_10

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  • DOI: https://doi.org/10.1007/978-3-540-74450-4_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74449-8

  • Online ISBN: 978-3-540-74450-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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