Equivalence between Extendibility and Factor-Criticality

In this paper, we show that if $k\geq (ν+2)/4$, where $ν$ denotes the order of a graph, a non-bipartite graph $G$ is $k$-extendable if and only if it is $2k$-factor-critical. If $k\geq (ν-3)/4$, a graph $G$ is $k\ 1/2$-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].

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