Construction of $k$-matchings and $k$-regular subgraphs in graph products

Anna Lindeberg, Marc Hellmuth

A $k$-matching $M$ of a graph $G=(V,E)$ is a subset $M\subseteq E$ such that each connected component in the subgraph $F=(V,M)$ of $G$ is either a single-vertex graph or $k$-regu…