Finding intersection models of weakly chordal graphs

Authors:
Martin Charles Golumbic;Marina Lipshteyn;Michal Stern
Affiliations:
Caesarea Rothschild Institute, University of Haifa, Haifa, Israel;Caesarea Rothschild Institute, University of Haifa, Haifa, Israel;Caesarea Rothschild Institute, University of Haifa, Haifa, Israel
Venue:
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Year:
2006

Citing 3
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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 (K2,3, , , , H1, H2, H3)-free 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.