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On economical set representations of graphs

Abstract : In this paper we discuss the bounds of and relations among various kinds of intersection numbers of graphs. Especially, we address extremal graphs with respect to the established bounds. The uniqueness of the minimum-size intersection representations for some graphs is also studied. In the course of this work, we introduce a superclass of chordal graphs, defined in terms of a generalization of simplicial vertex and perfect elimination ordering.
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Jing Kong, Yaokun Wu. On economical set representations of graphs. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2009, 11 (2), pp.71--95. ⟨hal-00988208⟩

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