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On the Recognition of P 4 -Comparability Graphs

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Graph-Theoretic Concepts in Computer Science (WG 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2573))

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Abstract

We consider the problem of recognizing whether a simple undirected graph is a P 4-comparability graph. This problem has been considered by Hoàng and Reed who described an O(n4)-time algorithm for its solution, where n is the number of vertices of the given graph. Faster algorithms have recently been presented by Raschle and Simon and by Nikolopoulos and Palios; the time complexity of both algorithms is O(n + m 2), where m is the number of edges of the graph. In this paper, we describe an O(nm)-time, O(n+m)-space algorithm for the recognition of P4-comparability graphs. The algorithm computes the P 4s of the input graph G by means of the BFS-trees of the complement of G rooted at each of its vertices, without however explicitly computing the complement of G. Our algorithm is simple, uses simple data structures, and leads to an O(n m)-time algorithm for computing an acyclic P 4- transitive orientation of a P 4-comparability graph.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Ioannina, GR-45110, Ioannina, Greece

    Stavros D. Nikolopoulos & Leonidas Palios

Authors
  1. Stavros D. Nikolopoulos
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  2. Leonidas Palios
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Editor information

Editors and Affiliations

  1. Karlsruhe University, Germany

    Gerhard Goos

  2. Cornell University, NY, USA

    Juris Hartmanis

  3. Utrecht University, The Netherlands

    Jan van Leeuwen

  4. Department of Applied Mathematics, Charles University, Malostranské nám. 25, 118 00, Prague, Czech Republic

    Luděk Kučera

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© 2002 Springer-Verlag Berlin Heidelberg

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Nikolopoulos, S.D., Palios, L. (2002). On the Recognition of P 4 -Comparability Graphs. In: Goos, G., Hartmanis, J., van Leeuwen, J., Kučera, L. (eds) Graph-Theoretic Concepts in Computer Science. WG 2002. Lecture Notes in Computer Science, vol 2573. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36379-3_31

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  • DOI: https://doi.org/10.1007/3-540-36379-3_31

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00331-1

  • Online ISBN: 978-3-540-36379-8

  • eBook Packages: Springer Book Archive

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