Maximum matchings in regular graphs
Abstract
It was conjectured by Mkrtchyan, Petrosyan, and Vardanyan that every graph G with (G)-δ(G) 1 has a maximum matching M such that any two M-unsaturated vertices do not share a neighbor. In this note, we confirm the conjecture for all k-regular simple graphs and also k-regular multigraphs with k 4.
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