On the clique-width of some perfect graph classes

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Graphs of clique-width at most k were introduced by Courcelle, 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, we show that for every in N there is a unit interval graph In and a permutation graph Hn having n2 vertices, each of whose clique-width is at least n. These results allow us 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×n square grid, in N, n ≥ 3, has clique-width exactly n+1.

Original languageEnglish
Pages (from-to)423-443
Number of pages21
JournalInternational Journal of Foundations of Computer Science
Issue number3
StatePublished - 2000
Externally publishedYes


  • Clique-width
  • distance hereditary graphs
  • permutation graphs
  • square grids
  • unit interval graphs

ASJC Scopus subject areas

  • Computer Science (miscellaneous)


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