## Abstract

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 I_{n} and a permutation graph H_{n} having n^{2} 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 language | English |
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Title of host publication | Graph-Theoretic Concepts in Computer Science - 25th International Workshop, WG 1999, Proceedings |

Editors | Peter Widmayer, Gabriele Neyer, Stephan Eidenbenz |

Publisher | Springer Verlag |

Pages | 135-147 |

Number of pages | 13 |

ISBN (Print) | 3540667318, 9783540667315 |

DOIs | |

State | Published - 1999 |

Externally published | Yes |

Event | 25th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 1999 - Ascona, Switzerland Duration: 17 Jun 1999 → 19 Jun 1999 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 1665 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 25th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 1999 |
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Country/Territory | Switzerland |

City | Ascona |

Period | 17/06/99 → 19/06/99 |

### Bibliographical note

Publisher Copyright:© Springer-Verlag Berlin Heidelberg 1999.

## ASJC Scopus subject areas

- Theoretical Computer Science
- General Computer Science