On totally unimodularity of edge-edge adjacency matrices

Yusuke Matsumoto, Naoyuki Kamiyama, Keiko Imai

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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.

Original languageEnglish
Title of host publicationComputing and Combinatorics - 17th Annual International Conference, COCOON 2011, Proceedings
Pages354-365
Number of pages12
DOIs
Publication statusPublished - Aug 29 2011
Externally publishedYes
Event17th Annual International Computing and Combinatorics Conference, COCOON 2011 - Dallas, TX, United States
Duration: Aug 14 2011Aug 16 2011

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6842 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other17th Annual International Computing and Combinatorics Conference, COCOON 2011
CountryUnited States
CityDallas, TX
Period8/14/118/16/11

Fingerprint

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

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Matsumoto, Y., Kamiyama, N., & Imai, K. (2011). On totally unimodularity of edge-edge adjacency matrices. In Computing and Combinatorics - 17th Annual International Conference, COCOON 2011, Proceedings (pp. 354-365). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6842 LNCS). https://doi.org/10.1007/978-3-642-22685-4_32

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

Computing and Combinatorics - 17th Annual International Conference, COCOON 2011, Proceedings. 2011. p. 354-365 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6842 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Matsumoto, Y, Kamiyama, N & Imai, K 2011, On totally unimodularity of edge-edge adjacency matrices. in Computing and Combinatorics - 17th Annual International Conference, COCOON 2011, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6842 LNCS, pp. 354-365, 17th Annual International Computing and Combinatorics Conference, COCOON 2011, Dallas, TX, United States, 8/14/11. https://doi.org/10.1007/978-3-642-22685-4_32
Matsumoto Y, Kamiyama N, Imai K. On totally unimodularity of edge-edge adjacency matrices. In Computing and Combinatorics - 17th Annual International Conference, COCOON 2011, Proceedings. 2011. p. 354-365. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-22685-4_32
Matsumoto, Yusuke ; Kamiyama, Naoyuki ; Imai, Keiko. / On totally unimodularity of edge-edge adjacency matrices. Computing and Combinatorics - 17th Annual International Conference, COCOON 2011, Proceedings. 2011. pp. 354-365 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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