Combining known results it follows that deciding whether a given graph G of size m has a unique perfect matching as well as finding that matching if it exists, can be done in time O(m) if G is either a cograph, or a split graph, or a claw-free graph. We provide structural insights concerning the graphs with a unique perfect matching that belong to these three graph classes, which lead to simple linear time algorithms for the unique perfect matching problem. (C) 2018 Elsevier B.V. All rights reserved.
|Journal||Information Processing Letters|
|Publication status||Published - 2018|