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:
Discrete Applied Mathematics
Year:
2009

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Abstract

We first present new structural properties of a two-pair in various graphs. A two-pair is used in a well-known characterization of weakly chordal graphs. Based on these properties, we prove the main theorem: a graph G is a weakly chordal (K"2","3,4P"2@?,P"2@?P"4@?,P"6@?,H"1,H"2,H"3)-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 an 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.