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Japanese Conference on Discrete and Computational Geometry and Graphs

JCDCGG 2013: Discrete and Computational Geometry and Graphs pp 138–144Cite as

The Double Multicompetition Number of a Multigraph

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8845))

Abstract

The double competition multigraph of a digraph \(D\) is the multigraph which has the same vertex set as \(D\) and has \(m_{xy}\) multiple edges between two distinct vertices \(x\) and \(y\), where \(m_{xy}\) is defined to be the number of common out-neighbors of \(x\) and \(y\) in \(D\) times the number of common in-neighbors of \(x\) and \(y\) in \(D\).

In this paper, we introduce the notion of the double multicompetition number of a multigraph. It is easy to observe that, for any multigraph \(M\), \(M\) together with sufficiently many isolated vertices is the double competition multigraph of some acyclic digraph. The double multicompetition number of a multigraph is defined to be the minimum number of such isolated vertices. We give a characterization of multigraphs with bounded double multicompetition number and give a lower bound for the double multicompetition numbers of multigraphs.

Yoshio Sano - This work was supported by JSPS KAKENHI grant number 25887007.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Pusan National University, Busan, 609-735, Korea

    Jeongmi Park

  2. Division of Information Engineering, Faculty of Engineering, Information and Systems, University of Tsukuba, Ibaraki, 305-8573, Japan

    Yoshio Sano

Authors
  1. Jeongmi Park
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  2. Yoshio Sano
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Correspondence to Yoshio Sano .

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Editors and Affiliations

  1. Tokyo University of Science, Tokyo, Japan

    Jin Akiyama

  2. The University of Electro-Communications, Tokyo, Japan

    Hiro Ito

  3. Tokai University, Tokyo, Japan

    Toshinori Sakai

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Park, J., Sano, Y. (2014). The Double Multicompetition Number of a Multigraph. In: Akiyama, J., Ito, H., Sakai, T. (eds) Discrete and Computational Geometry and Graphs. JCDCGG 2013. Lecture Notes in Computer Science(), vol 8845. Springer, Cham. https://doi.org/10.1007/978-3-319-13287-7_12

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  • DOI: https://doi.org/10.1007/978-3-319-13287-7_12

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-13286-0

  • Online ISBN: 978-3-319-13287-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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