The matching preclusion number of a graph is the minimum number of edges whose deletion resultsinagraph that has neither perfect matchings nor almost-perfect matchings. For many interconnection networks, the optimal sets are precisely those inducedby asingle 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 this number and classify all optimal sets for the arrangement graphs, one of the most popular interconnection networks.
Bibliographical noteFunding Information:
The research was partially supported by the NSF-REU under Grant DMS 0649099.
- Arrangement graphs
- Interconnection networks
- Perfect matching