论文信息 - A Generalization of Chordal Graphs and the Maximum Clique Problem

A Generalization of Chordal Graphs and the Maximum Clique Problem

Abstract A graph is chordal or triangulated if it has no chordless cycle with four or more vertices. Chordal graphs are well known for their combinatorial and algorithmic properties. Here we introduce a generalization of chordal graphs, namely CSGk graphs. Informally, a CSG0 graph is a complete graph, and for k s> 0, the class of CSGk graphs is defined inductively in a such manner that CSG1 Graphs are chordal graphs. We show that CSGk Graphs inherit of the same kind of properties as chordal graph. As a consequence, we show that the maximum clique problem is polynomial on CSGk graphs while this problem is NP-hard in the general case.

Philippe Jégou | Assef Chmeiss

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