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International Computing and Combinatorics Conference

COCOON 2011: Computing and Combinatorics pp 354–365Cite as

On Totally Unimodularity of Edge-Edge Adjacency Matrices

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6842))

Abstract

We consider totally unimodularity for edge-edge adjacency matrices which represent a relationship between two edges in a graph. The matrices appear in integer programming formulations for the minimum maximal matching problem and the edge dominating set problem.

We consider a problem of characterizing graphs having totally unimodular matrices as their edge-edge adjacency matrices, and give a necessary and sufficient condition for the characterization. The condition is the first characterization for edge-edge adjacency matrices.

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References

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Author information

Authors and Affiliations

  1. IBM Software Group, Japan

    Yusuke Matsumoto

  2. Department of Information and System Engineering, Chuo University, Japan

    Naoyuki Kamiyama & Keiko Imai

Authors
  1. Yusuke Matsumoto
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  2. Naoyuki Kamiyama
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  3. Keiko Imai
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Texas-Pan American, 78539, Edinburg, TX, USA

    Bin Fu

  2. Department of Computer Science, University of Texas at Dallas, 75080, Richardson, TX, USA

    Ding-Zhu Du

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© 2011 Springer-Verlag Berlin Heidelberg

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Matsumoto, Y., Kamiyama, N., Imai, K. (2011). On Totally Unimodularity of Edge-Edge Adjacency Matrices. In: Fu, B., Du, DZ. (eds) Computing and Combinatorics. COCOON 2011. Lecture Notes in Computer Science, vol 6842. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22685-4_32

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  • DOI: https://doi.org/10.1007/978-3-642-22685-4_32

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22684-7

  • Online ISBN: 978-3-642-22685-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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