On totally unimodularity of edge-edge adjacency matrices

Authors:
Yusuke Matsumoto;Naoyuki Kamiyama;Keiko Imai
Affiliations:
IBM Software Group, Japan;Department of Information and System Engineering, Chuo University, Japan;Department of Information and System Engineering, Chuo University, Japan
Venue:
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
Year:
2011

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Abstract

We consider totally unimodularity for edge-edge adjacency matrices which represent a relationship between two edges in a graph. The matrices appear in integer programming formulations for the minimum maximal matching problem and the edge dominating set problem. We consider a problem of characterizing graphs having totally unimodular matrices as their edge-edge adjacency matrices, and give a necessary and sufficient condition for the characterization. The condition is the first characterization for edge-edge adjacency matrices.