%0 Journal Article
%A Yi-pei ZHANG
%A Xiu-mei WANG
%A Jin-jiang YUAN
%T PM-compact Graphs and Vertex-deleted Subgraphs
%D 2022
%R 10.1007/s10255-022-1018-3
%J 应用数学学报(英文版)
%P 955-965
%V 38
%N 4
%X 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.
%U https://applmath.cjoe.ac.cn/jweb_yysxxb_en/CN/10.1007/s10255-022-1018-3