On perfect k-matchings
Hongliang Lu
TL;DR
This paper extends the concept of perfect matchings to perfect k-matchings, providing necessary and sufficient conditions for their existence in various graph classes, including bipartite and regular graphs.
Contribution
It introduces a generalized framework for perfect k-matchings and establishes new conditions for their existence in bipartite and regular graphs.
Findings
Equivalence of k-matching problem to matching question in bipartite graphs
Necessary and sufficient conditions for perfect k-matchings
Sufficient conditions based on edge connectivity in regular graphs
Abstract
In this paper, we generalize the notions of perfect matchings, perfect 2-matchings to perfect k-matchings and give a necessary and sufficient condition for existence of perfect k-matchings. For bipartite graphs, we show that this k-matching problem is equivalent to that matching question. Moreover, for regular graphs, we provide a sufficient condition of perfect k-matching in terms of edge connectivity.
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Taxonomy
TopicsCooperative Communication and Network Coding · Mobile Ad Hoc Networks · Complexity and Algorithms in Graphs