Dominating induced matchings in graphs containing no long claw

Dominating induced matchings in graphs containing no long claw An induced matching M in a graph G is dominating if every edge not in M shares exactly one vertex with an edge in M. The dominating induced matching problem (also known as efficient edge domination) asks whether a graph G contains a dominating induced matching. This problem is generally NP‐complete, but polynomial‐time solvable for graphs with some special properties. In particular, it is solvable in polynomial time for claw‐free graphs. In the present article, we provide a polynomial‐time algorithm to solve the dominating induced matching problem for graphs containing no long claw, that is, no induced subgraph obtained from the claw by subdividing each of its edges exactly once. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Graph Theory Wiley

Dominating induced matchings in graphs containing no long claw

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Publisher
Wiley Subscription Services, Inc., A Wiley Company
Copyright
Copyright © 2018 Wiley Periodicals, Inc.
ISSN
0364-9024
eISSN
1097-0118
D.O.I.
10.1002/jgt.22182
Publisher site
See Article on Publisher Site

Abstract

An induced matching M in a graph G is dominating if every edge not in M shares exactly one vertex with an edge in M. The dominating induced matching problem (also known as efficient edge domination) asks whether a graph G contains a dominating induced matching. This problem is generally NP‐complete, but polynomial‐time solvable for graphs with some special properties. In particular, it is solvable in polynomial time for claw‐free graphs. In the present article, we provide a polynomial‐time algorithm to solve the dominating induced matching problem for graphs containing no long claw, that is, no induced subgraph obtained from the claw by subdividing each of its edges exactly once.

Journal

Journal of Graph TheoryWiley

Published: Jan 1, 2018

Keywords: ; ;

References

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