Matchings Defined by Local Conditions
نویسندگان
چکیده
A graph has the neighbour-closed-co-neighbour, or ncc property, if for each of its vertices x, the subgraph induced by the neighbour set of x is isomorphic to the subgraph induced by the closed non-neighbour set of x. Graphs with the ncc property were characterized in [1] by the existence of a locally C4 perfect matching M : every two edges of M induce a subgraph isomorphic to C4. In the present article, we investigate variants of locally C4 perfect matchings. We consider the cases where pairs of distinct edges of the matching induce isomorphism types including P4, the paw, or the diamond. We give several characterizations of graphs with such matchings. In addition, we supply characterizations of graphs with matchings whose edges satisfy a prescribed parity condition.
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