摘要
The perfect matching polytope of a graph G is the convex hull of the incidence vectors of all perfect matchings of G.A graph G is PM-compact if the 1-skeleton graph of the prefect matching polytope of G is complete.Equivalently,a matchable graph G is PM-compact if and only if for each even cycle C of G,G-V(C)has at most one perfect matching.This paper considers the class of graphs from which deleting any two adjacent vertices or nonadjacent vertices,respectively,the resulting graph has a unique perfect matching.The PM-compact graphs in this class of graphs are presented.
基金
supported by the National Natural Science Foundation of China(Nos.12171440,11971445)。
