Uniquely restricted matchings in interval graphs

Authors

Mathew C. Francis, Indian Statistical Institute Chennai
Dalu Jacob, Indian Statistical Institute Chennai
Satyabrata Jana, Indian Statistical Institute, Kolkata

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

Recommended Citation

Francis, Mathew C.; Jacob, Dalu; and Jana, Satyabrata, "Uniquely restricted matchings in interval graphs" (2018). Journal Articles. 1581.
https://digitalcommons.isical.ac.in/journal-articles/1581