On the clique—width of perfect graph classes

Martin Charles Golumbic; Udi Rotics

doi:10.1007/3-540-46784-x_14

On the clique—width of perfect graph classes

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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 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 language	English
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	https://doi.org/10.1007/3-540-46784-x_14
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)
Volume	1665
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	25th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 1999
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

Access to Document

10.1007/3-540-46784-x_14

Cite this

Golumbic, M. C., & Rotics, U. (1999). On the clique—width of perfect graph classes. In P. Widmayer, G. Neyer, & S. Eidenbenz (Eds.), Graph-Theoretic Concepts in Computer Science - 25th International Workshop, WG 1999, Proceedings (pp. 135-147). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1665). Springer Verlag. https://doi.org/10.1007/3-540-46784-x_14

Golumbic, Martin Charles ; Rotics, Udi. / On the clique—width of perfect graph classes. Graph-Theoretic Concepts in Computer Science - 25th International Workshop, WG 1999, Proceedings. editor / Peter Widmayer ; Gabriele Neyer ; Stephan Eidenbenz. Springer Verlag, 1999. pp. 135-147 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "On the clique—width of perfect graph classes",

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 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.",

author = "Golumbic, {Martin Charles} and Udi Rotics",

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year = "1999",

doi = "10.1007/3-540-46784-x_14",

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series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

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Golumbic, MC & Rotics, U 1999, On the clique—width of perfect graph classes. in P Widmayer, G Neyer & S Eidenbenz (eds), Graph-Theoretic Concepts in Computer Science - 25th International Workshop, WG 1999, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1665, Springer Verlag, pp. 135-147, 25th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 1999, Ascona, Switzerland, 17/06/99. https://doi.org/10.1007/3-540-46784-x_14

On the clique—width of perfect graph classes. / Golumbic, Martin Charles; Rotics, Udi.
Graph-Theoretic Concepts in Computer Science - 25th International Workshop, WG 1999, Proceedings. ed. / Peter Widmayer; Gabriele Neyer; Stephan Eidenbenz. Springer Verlag, 1999. p. 135-147 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1665).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

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AU - Golumbic, Martin Charles

AU - Rotics, Udi

N1 - Publisher Copyright: © Springer-Verlag Berlin Heidelberg 1999.

PY - 1999

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N2 - 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.

AB - 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.

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SN - 9783540667315

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

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PB - Springer Verlag

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Y2 - 17 June 1999 through 19 June 1999

ER -

Golumbic MC, Rotics U. On the clique—width of perfect graph classes. In Widmayer P, Neyer G, Eidenbenz S, editors, Graph-Theoretic Concepts in Computer Science - 25th International Workshop, WG 1999, Proceedings. Springer Verlag. 1999. p. 135-147. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/3-540-46784-x_14

On the clique—width of perfect graph classes

Abstract

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Bibliographical note

ASJC Scopus subject areas

Access to Document

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