Article ID: | iaor20134083 |
Volume: | 67 |
Issue: | 2 |
Start Page Number: | 277 |
End Page Number: | 292 |
Publication Date: | Oct 2013 |
Journal: | Algorithmica |
Authors: | Imai Keiko, Kamiyama Naoyuki, Matsumoto Yusuke |
Keywords: | matrices, programming: integer |
We consider total unimodularity for edge–edge adjacency matrices that represent adjacency relations between pairs of edges in a graph. These matrices appear in integer programming formulations of the minimum maximal matching problem, the edge dominating set problem, and so on. We investigate the problem of characterizing graphs that have totally unimodular edge–edge adjacency matrices, and give a necessary and sufficient condition for characterization. This condition is the first characterization for total unimodularity of edge–edge adjacency matrices.