On total unimodularity of edge-edge adjacency matrices

Yusuke Matsumoto, Naoyuki Kamiyama, Keiko Imai

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)277-292
Number of pages16
JournalAlgorithmica
Volume67
Issue number2
DOIs
Publication statusPublished - Oct 1 2013

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Adjacency Matrix
Adjacency
Dominating Set
Matching Problem
Graph in graph theory
Integer Programming
Integer programming
Necessary Conditions
Formulation
Sufficient Conditions

All Science Journal Classification (ASJC) codes

  • Computer Science(all)
  • Computer Science Applications
  • Applied Mathematics

Cite this

On total unimodularity of edge-edge adjacency matrices. / Matsumoto, Yusuke; Kamiyama, Naoyuki; Imai, Keiko.

In: Algorithmica, Vol. 67, No. 2, 01.10.2013, p. 277-292.

Research output: Contribution to journalArticle

Matsumoto, Yusuke ; Kamiyama, Naoyuki ; Imai, Keiko. / On total unimodularity of edge-edge adjacency matrices. In: Algorithmica. 2013 ; Vol. 67, No. 2. pp. 277-292.
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