Title

Uniquely restricted matchings in interval graphs

Article Type

Research Article

Publication Title

SIAM Journal on Discrete Mathematics

Abstract

A matching M in a graph G is said to be uniquely restricted if there is no other matching in G that matches the same set of vertices as M. We describe a polynomial-time algorithm to compute a maximum cardinality uniquely restricted matching in an interval graph, thereby answering a question of Golumbic, Hirst, and Lewenstein [Algorithmica, 31 (2001), pp. 139–154]. Our algorithm actually solves the more general problem of computing a maximum cardinality “weak independent set” in an interval nest digraph, which may be of independent interest. Further, we give linear-time algorithms for computing maximum cardinality uniquely restricted matchings in proper interval graphs and bipartite permutation graphs.

First Page

148

Last Page

172

DOI

10.1137/16M1074631

Publication Date

1-1-2018

Comments

All Open Access, Green

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