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.
|Title of host publication||Graph-Theoretic Concepts in Computer Science - 25th International Workshop, WG 1999, Proceedings|
|Editors||Peter Widmayer, Gabriele Neyer, Stephan Eidenbenz|
|Number of pages||13|
|ISBN (Print)||3540667318, 9783540667315|
|State||Published - 1999|
|Event||25th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 1999 - Ascona, Switzerland|
Duration: 17 Jun 1999 → 19 Jun 1999
|Name||Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)|
|Conference||25th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 1999|
|Period||17/06/99 → 19/06/99|
Bibliographical notePublisher Copyright:
© Springer-Verlag Berlin Heidelberg 1999.
ASJC Scopus subject areas
- Theoretical Computer Science
- Computer Science (all)