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On Module-Composed Graphs

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Graph-Theoretic Concepts in Computer Science (WG 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5911))

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Abstract

In this paper we introduce module-composed graphs, i.e. graphs which can be defined by a sequence of one-vertex insertions v 1,...,v n , such that the neighbourhood of vertex v i , 2 ≤ i ≤ n, forms a module of the graph defined by vertices v 1,...,v i − 1.

We show that module-composed graphs are HHDS-free and thus homogeneously orderable, weakly chordal, and perfect. Every bipartite distance hereditary graph and every trivially perfect graph is module- composed. We give an \(\mathcal{O}(|V|\cdot (|V|+|E|))\) time algorithm to decide whether a given graph G = (V,E) is module-composed and construct a corresponding module-sequence.

For the case of bipartite graphs, we show that the set of module-composed graphs is equivalent to the well known class of distance hereditary graphs, which implies linear time algorithms for their recognition and construction of a corresponding module-sequence using BFS and Lex-BFS.

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Authors and Affiliations

  1. Institute of Computer Science, Heinrich-Heine-University Düsseldorf, D-40225, Düsseldorf, Germany

    Frank Gurski & Egon Wanke

Authors
  1. Frank Gurski
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  2. Egon Wanke
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Editors and Affiliations

  1. CNRS - LIRMM, 161 rue Ada, 34392, Montpellier Cedex 5, France

    Christophe Paul

  2. LIAFA, case 7014, Université Paris Diderot, 75205, Paris Cedex 13, France

    Michel Habib

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Gurski, F., Wanke, E. (2010). On Module-Composed Graphs. In: Paul, C., Habib, M. (eds) Graph-Theoretic Concepts in Computer Science. WG 2009. Lecture Notes in Computer Science, vol 5911. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11409-0_15

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  • DOI: https://doi.org/10.1007/978-3-642-11409-0_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-11408-3

  • Online ISBN: 978-3-642-11409-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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