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Recognizing Polar Planar Graphs Using New Results for Monopolarity

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Algorithms and Computation (ISAAC 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7074))

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Abstract

Polar and monopolar graphs are natural generalizations of bipartite or split graphs. A graph G = (V,E) is polar if its vertex set admits a partition V = A ∪ B such that A induces a complete multipartite and B the complement of a complete multipartite graph. If A is even a stable set then G is called monopolar.

Recognizing general polar or monopolar graphs is NP-complete and, as yet, efficient recognition is available only for very few graph classes.

This paper considers monopolar and polar graphs that are also planar. On the one hand, we show that recognizing these graphs remains NP-complete, on the other hand we identify subclasses of planar graphs on which polarity and monopolarity can be checked efficiently. The new NP-completeness results cover very restricted graph classes and are sharper than all previous known cases. On the way to the positive results, we develop new techniques for efficient recognition of subclasses of monopolar graphs. These new results extend nearly all known results for efficient monopolar recognition.

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Author information

Authors and Affiliations

  1. University of Rostock, Germany

    Van Bang Le & Ragnar Nevries

Authors
  1. Van Bang Le
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  2. Ragnar Nevries
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Editor information

Editors and Affiliations

  1. Chuo University, Kasuga, Bunkyo-ku, 112-8551, Tokyo, Japan

    Takao Asano

  2. Gunma University, 1-5-1 Tenjin-Cho, 376-8515, Kiryu-Shi, Japan

    Shin-ichi Nakano

  3. Japan Advanced Institute of Science and Technology, 1-1 Asahidai, 923-1292, Nomi, Ishikawa, Japan

    Yoshio Okamoto

  4. Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, 152-8552, Tokyo, Japan

    Osamu Watanabe

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© 2011 Springer-Verlag Berlin Heidelberg

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Le, V.B., Nevries, R. (2011). Recognizing Polar Planar Graphs Using New Results for Monopolarity. In: Asano, T., Nakano, Si., Okamoto, Y., Watanabe, O. (eds) Algorithms and Computation. ISAAC 2011. Lecture Notes in Computer Science, vol 7074. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25591-5_14

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  • DOI: https://doi.org/10.1007/978-3-642-25591-5_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-25590-8

  • Online ISBN: 978-3-642-25591-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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