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Recognizing Planar Strict Quasi-Parity Graphs

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Abstract.

 A graph is a strict-quasi parity (SQP) graph if every induced subgraph that is not a clique contains a pair of vertices with no odd chordless path between them (an “even pair”). We present an O(n 3) algorithm for recognizing planar strict quasi-parity graphs, based on Wen-Lian Hsu's decomposition of planar (perfect) graphs and on the (non-algorithmic) characterization of planar minimal non-SQP graphs given in [9].

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Authors and Affiliations

  1. Universidade Federal do Ceará, Rua Deputado Moreira da Rocha 380, 601, Meireles, Fortaleza-CE, CEP 60160-060, Brazil. e-mail: linhares@lia.ufc.br, , , , , , BR

    Cláudia Linhares Sales

  2. CNRS, Laboratoire Leibniz-IMAG, 46 avenue Félix Viallet, 38031 Grenoble Cedex, France, , , , , , FR

    Frédéric Maffray

  3. CNRS, Equipe Combinatoire, Université Pierre et Marie Curie, 4 place Jussieu, 75005 Paris, France, , , , , , FR

    Bruce Reed

Authors
  1. Cláudia Linhares Sales
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  2. Frédéric Maffray
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  3. Bruce Reed
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Received: September 21, 1998 Final version received: May 9, 2000

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Sales, C., Maffray, F. & Reed, B. Recognizing Planar Strict Quasi-Parity Graphs. Graphs Comb 17, 745–757 (2001). https://doi.org/10.1007/s003730170014

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  • DOI: https://doi.org/10.1007/s003730170014

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