Fractional matching preclusion for arrangement graphs

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. As a generalization, Liu and Liu (2017) recently introduced the concept of fractional matching preclusion number. The fractional matching preclusion number (FMP number) of G is the minimum number of edges whose deletion leaves the resulting graph without a fractional perfect matching. The fractional strong matching preclusion number (FSMP number) of G is the minimum number of vertices and edges whose deletion leaves the resulting graph without a fractional perfect matching. In this paper, we obtain the FMP number and the FSMP number for arrangement graphs. In addition, all the optimal fractional strong matching preclusion sets of these graphs are categorized.