Geodesic
On k-factor-critical graphs
Discussiones Mathematicae. Graph Theory, Tome 16 (1996) no. 1, pp. 41-51

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A graph is said to be k-factor-critical if the removal of any set of k vertices results in a graph with a perfect matching. We study some properties of k-factor-critical graphs and show that many results on q-extendable graphs can be improved using this concept.
Keywords: matching, extendable, factor 
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Favaron, Odile. On k-factor-critical graphs. Discussiones Mathematicae. Graph Theory, Tome 16 (1996) no. 1, pp. 41-51. http://geodesic.mathdoc.fr/item/DMGT_1996_16_1_a3/