MATCHING PRECLUSION AND CONDITIONAL MATCHING PRECLUSION FOR CROSSED CUBES

Abstract

The matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost-perfect matchings. For many interconnection networks, the optimal sets are precisely those induced by a single vertex. Recently, the conditional matching preclusion number of a graph was introduced to look for obstruction sets beyond those induced by a single vertex. It is defined to be the minimum number of edges whose deletion results in a graph with no isolated vertices that has neither perfect matchings nor almost-perfect matchings. In this paper, we find the matching preclusion number and the conditional matching preclusion number with the classification of the optimal sets for the class of crossed cubes, an important variant of the class of hypercubes. Indeed, we will establish more general results on the matching preclusion and the conditional matching preclusion problems for a larger class of interconnection networks.