On the clique—width of perfect graph classes

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Graphs of clique-width at most k were introduced by Cour-celle, Engelfriet and Rozenberg (1993) as graphs which can be defined by k-expressions based on graph operations which use k vertex labels. In this paper we study the clique-width of perfect graph classes. On one hand, we show that every distance-hereditary graph, has clique-width at most 3, and a 3-expression defining it can be obtained in linear time. On the other hand, we show that the classes of unit interval and permutation graphs are not of bounded clique-width. More precisely, weshow that forevery n ɛ Ɲ there is a unit interval graph In and a permutation graph Hn having n2 vertices, each of whose clique-width is exactly n+1. These results allowus to see the border within the hierarchy of perfect graphs between classes whose clique-width is bounded and classes whose clique-width is unbounded. Finally we show that every n x n square grid, n ɛ Ɲ, n ≥ 3, has clique-width exactly n + 1.

Original languageEnglish
Title of host publicationGraph-Theoretic Concepts in Computer Science - 25th International Workshop, WG 1999, Proceedings
EditorsPeter Widmayer, Gabriele Neyer, Stephan Eidenbenz
PublisherSpringer Verlag
Number of pages13
ISBN (Print)3540667318, 9783540667315
StatePublished - 1999
Externally publishedYes
Event25th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 1999 - Ascona, Switzerland
Duration: 17 Jun 199919 Jun 1999

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference25th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 1999

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1999.

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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