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A Characterization of Graphs with Vertex Cover Six

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Computing and Combinatorics (COCOON 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1858))

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Abstract

The complete list of forbidden minors (obstructions) for the family of graphs with vertex cover 6 have been found. This paper shows how one can limit the search space of graphs and how to simplify the process for deciding whether a graph is an obstruction for k-Vertex Cover. The upper bounds 2k + 1 (2k + 2) on the maximum number of vertices for connected (disconnected) obstructions are shown to be sharp for all k > 0.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Auckland, Private Bag 92019, Auckland, New Zealand

    Michael J. Dinneen & Liu Xiong

Authors
  1. Michael J. Dinneen
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  2. Liu Xiong
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, University of Minnesota, MN 55455, Minneapolis, USA

    Ding-Zhu Du

  2. Department of Computer Science and Software Engineering, University of Newcastle, Callaghan, NSW 2308, Australia

    Peter Eades  & Vladimir Estivill-Castro  & 

  3. School of Computer Science and Engineering, University of Newcastle, NSW 2052, Sydney, Australia

    Xuemin Lin  & Arun Sharma  & 

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Dinneen, M.J., Xiong, L. (2000). A Characterization of Graphs with Vertex Cover Six. In: Du, DZ., Eades, P., Estivill-Castro, V., Lin, X., Sharma, A. (eds) Computing and Combinatorics. COCOON 2000. Lecture Notes in Computer Science, vol 1858. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44968-X_18

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  • DOI: https://doi.org/10.1007/3-540-44968-X_18

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67787-1

  • Online ISBN: 978-3-540-44968-3

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