The strong matching preclusion number of a graph is the minimum number of vertices and edges whose deletion results in a graph that has neither perfect matchings nor almost-perfect matchings. This is an extension of the matching preclusion problem that was introduced by Park and Ihm. The class of arrangement graphs was introduced as a common generalization of star graphs and alternating group g...

The matching preclusion number of an even graph is the minimum number of edges whose deletion results in a graph that has no perfect matchings. For many interconnection networks, the optimal sets are precisely those induced by a single vertex. Recently, the conditional matching preclusion number of an even graph was introduced to look for obstruction sets beyond those induced by a single vertex...

The method of graphical condensation for enumerating perfect matchings was found by Propp (Theoretical Computer Science 303(2003), 267-301), and was generalized by Kuo (Theoretical Computer Science 319 (2004), 29-57). In this paper, we obtain some more general results on graphical condensation than Kuo’s. Our method is also different from Kuo’s. As applications of our results, we obtain a new p...