Equivalence between Extendibility and Factor-Criticality

Abstract

In this paper, we show that if $k\ge \frac{v+2}{4}$, where $v$ denotes the order of a graph, a non-bipartite graph $G$ is $k$-extendable if and only if it is $2k$-factor-critical. If $k\ge \frac{v-3}{4}$, a graph $G$ is $k$-extendable if and only if it is $(2k+1)$-factor-critical. We also give examples to show that the two bounds are best possible. Our results are answers to a problem posted by Favaron $[3]$ and Yu $[11]$.