Geodesic
Factor-criticality and matching extension in DCT-graphs
Discussiones Mathematicae. Graph Theory, Tome 17 (1997) no. 2, pp. 271-278

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The class of DCT-graphs is a common generalization of the classes of almost claw-free and quasi claw-free graphs. We prove that every even (2p+1)-connected DCT-graph G is p-extendable, i.e., every set of p independent edges of G is contained in a perfect matching of G. This result is obtained as a corollary of a stronger result concerning factor-criticality of DCT-graphs.
Keywords: factor-criticality, matching extension, claw, dominated claw toes 
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Favaron, Odile; Favaron, Evelyne; Ryjáček, Zdenĕk. Factor-criticality and matching extension in DCT-graphs. Discussiones Mathematicae. Graph Theory, Tome 17 (1997) no. 2, pp. 271-278. http://geodesic.mathdoc.fr/item/DMGT_1997_17_2_a5/