Finding intersection models of weakly chordal graphs

Martin Charles Golumbic; Marina Lipshteyn; Michal Stern

doi:10.1007/11917496_22

Finding intersection models of weakly chordal graphs

Martin Charles Golumbic, Marina Lipshteyn, Michal Stern

Department of Computer Science

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

Abstract

We first present new structural properties of a two-pair in various graphs. A two-pair is used for characterizing weakly chordal graphs. Based on these properties, we prove the main theorem: a graph G is a weakly chordal (K _2,3, P₆, 4P₂, P₂ ∪ P ₄, H₁, H₁, H₃)-bee graph if and only if G is an edge intersection graph of subtrees on a tree with maximum degree 4. This characterizes the so called [4, 4, 2] graphs. The proof of the theorem constructively finds the representation. Thus, we obtain a algorithm to construct an edge intersection model of subtrees on a tree with maximum degree 4 for such a given graph. This is a recognition algorithm for [4, 4, 2] graphs.

Original language	English
Title of host publication	Graph-Theoretic Concepts in Computer Science - 32nd International Workshop, WG 2006, Revised Papers
Publisher	Springer Verlag
Pages	241-255
Number of pages	15
ISBN (Print)	3540483810, 9783540483816
DOIs	https://doi.org/10.1007/11917496_22
State	Published - 2006
Event	32nd International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2006 - Bergen, Norway Duration: 22 Jun 2006 → 24 Jun 2006

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	4271 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	32nd International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2006
Country/Territory	Norway
City	Bergen
Period	22/06/06 → 24/06/06

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/11917496_22

Cite this

Golumbic, M. C., Lipshteyn, M., & Stern, M. (2006). Finding intersection models of weakly chordal graphs. In Graph-Theoretic Concepts in Computer Science - 32nd International Workshop, WG 2006, Revised Papers (pp. 241-255). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4271 LNCS). Springer Verlag. https://doi.org/10.1007/11917496_22

Golumbic, Martin Charles ; Lipshteyn, Marina ; Stern, Michal. / Finding intersection models of weakly chordal graphs. Graph-Theoretic Concepts in Computer Science - 32nd International Workshop, WG 2006, Revised Papers. Springer Verlag, 2006. pp. 241-255 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "We first present new structural properties of a two-pair in various graphs. A two-pair is used for characterizing weakly chordal graphs. Based on these properties, we prove the main theorem: a graph G is a weakly chordal (K 2,3, P6, 4P2, P2 ∪ P 4, H1, H1, H3)-bee graph if and only if G is an edge intersection graph of subtrees on a tree with maximum degree 4. This characterizes the so called [4, 4, 2] graphs. The proof of the theorem constructively finds the representation. Thus, we obtain a algorithm to construct an edge intersection model of subtrees on a tree with maximum degree 4 for such a given graph. This is a recognition algorithm for [4, 4, 2] graphs.",

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Golumbic, MC, Lipshteyn, M & Stern, M 2006, Finding intersection models of weakly chordal graphs. in Graph-Theoretic Concepts in Computer Science - 32nd International Workshop, WG 2006, Revised Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4271 LNCS, Springer Verlag, pp. 241-255, 32nd International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2006, Bergen, Norway, 22/06/06. https://doi.org/10.1007/11917496_22

Finding intersection models of weakly chordal graphs. / Golumbic, Martin Charles; Lipshteyn, Marina; Stern, Michal.
Graph-Theoretic Concepts in Computer Science - 32nd International Workshop, WG 2006, Revised Papers. Springer Verlag, 2006. p. 241-255 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4271 LNCS).

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

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Golumbic MC, Lipshteyn M, Stern M. Finding intersection models of weakly chordal graphs. In Graph-Theoretic Concepts in Computer Science - 32nd International Workshop, WG 2006, Revised Papers. Springer Verlag. 2006. p. 241-255. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/11917496_22

Finding intersection models of weakly chordal graphs

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