On Cartesian Product of Factor-Critical Graphs

A graph G is k-factor-critical if G ? S has a perfect matching for any k-subset S of V(G). In this paper, we investigate the factor-criticality in Cartesian products of graphs and show that Cartesian product of an m-factor-critical graph and an n-factor-critical graph is ${(m+n+\varepsilon )}$ -factor-critical, where ${\varepsilon = 0}$ if both of m and n are even; ${\varepsilon = 1}$ , otherwise. Moreover, this result is best possible.