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, \(\overline{P_6}\), \(\overline{4P_2}\), \(\overline{P_2 \cup P_4}\), 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 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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© 2006 Springer-Verlag Berlin Heidelberg
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Golumbic, M.C., Lipshteyn, M., Stern, M. (2006). Finding Intersection Models of Weakly Chordal Graphs. In: Fomin, F.V. (eds) Graph-Theoretic Concepts in Computer Science. WG 2006. Lecture Notes in Computer Science, vol 4271. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11917496_22
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DOI: https://doi.org/10.1007/11917496_22
Publisher Name: Springer, Berlin, Heidelberg
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