Extendability and factor-criticality (Q1970705)

A graph \(G\) is is said to be \(p\)-factor-critical if \(G-S\) has a perfect matching for each \(S\subset V(G)\) with \(|S|=p\). A graph \(G\) is \(p\)-extendable if any set of \(p\) independent edges is contained in a perfect matching. The author shows that for even \(p\) every non-bipartite \(p\)-extendable graph of even order is \(p\)-factor-critical, and every non-bipartite \((p+1)\)-extendable graph of even order is such that \(G-e\) is \(p\)-factor-critical for every edge \(e\in E(G)\). This generalizes results of \textit{M. D. Plummer} [On \(n\)-extendable graphs, Discrete Math. 31, No. 2, 201-210 (1980; Zbl 0442.05060)] on bicritical graphs.