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The subject of the paywalled article The minimum cost perfect matching problem with conflict pair constraints (MCPMPC) are perfect matchings of minimum cost that do not contain certain pairs of edges; ...

I am considering the following variant of the path-cover problem. I have an acyclic directed graph G=(V,E). Moreover, the set V is partitioned into $V=V_1 \cup ... \cup V_k$ (these sets are pairwise ...

Fedor Petrov has posed a notorious problem regarding the existence of a matching in this question: Resolution of multiple edges As I see it the setting is a constrained bipartite matching and thus, ...