Intersection models of weakly chordal graphs

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 GG is a weakly chordal (K2,3,4P2¯,P2∪P4¯,P6¯,H1,H2,H3)-free graph if and only if GG 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.