Matroid Representation of Clique Complexes

In this paper, we approach the quality of a greedy algorithm for the maximum weighted clique problem from the viewpoint of matroid theory. More precisely, we consider the clique complex of a graph (the collection of all cliques of the graph) which is also called a flag complex, and investigate the minimum number k such that the clique complex of a given graph can be represented as the intersection of k matroids. This number k can be regarded as a measure of “how complex a graph is with respect to the maximum weighted clique problem” since a greedy algorithm is a k-approximation algorithm for this problem. For any k > 0, we characterize graphs whose clique complexes can be represented as the intersection of k matroids. As a consequence, we can see that the class of clique complexes is the same as the class of the intersections of partition matroids. Moreover, we determine how many matroids are

• Type: Conference
• Year: 2003
• Where: COCOON
• Authors: Kenji Kashiwabara, Yoshio Okamoto, Takeaki Uno
• Keywords: Clique, Clique Problem, COCOON 2003, Maximum Weighted Clique