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/

[1] V. N. Bhat and S. F. Kapoor, The Powers of a Connected Graph are Highly Hamiltonian, Journal of Research of the National Bureau of Standards, Section B 75 (1971) 63-66.

[2] G. Chartrand, S. F. Kapoor and D. R. Lick, n-Hamiltonian Graphs, J. Combin. Theory 9 (1970) 308-312, doi: 10.1016/S0021-9800(70)80069-2.

[3] O. Favaron, Stabilité, domination, irredondance et autres parametres de graphes, These d'Etat, Université de Paris-Sud, 1986.

[4] O. Favaron, E. Flandrin and Z. Ryjáek, Factor-criticality and matching extension in DCT-graphs, Preprint.

[5] T. Gallai, Neuer Beweis eines Tutte'schen Satzes, Magyar Tud. Akad. Mat. Kutató Int. Közl. 8 (1963) 135-139.

[6] L. Lovász, On the structure of factorizable graphs, Acta Math. Acad. Sci. Hungar. 23 (1972) 179-195, doi: 10.1007/BF01889914.

[7] L. Lovász and M. D. Plummer, Matching Theory, Annals of Discrete Math. 29 (1986).

[8] M. Paoli, W. W. Wong and C. K. Wong, Minimum k-Hamiltonian Graphs II, J. Graph Theory 10 (1986) 79-95, doi: 10.1002/jgt.3190100111.

[9] M. D. Plummer, On n-extendable graphs, Discrete Math. 31 (1980) 201-210, doi: 10.1016/0012-365X(80)90037-0.

[10] M. D. Plummer, Toughness and matching extension in graphs, Discrete Math. 72 (1988) 311-320, doi: 10.1016/0012-365X(88)90221-X.

[11] M. D. Plummer, Degree sums, neighborhood unions and matching extension in graphs, in: R. Bodendiek, ed., Contemporary Methods in Graph Theory (B. I. Wiessenschaftsverlag, Mannheim, 1990) 489-502.

[12] M. D. Plummer, Extending matchings in graphs: A survey, Discrete Math. 127 (1994) 277-292, doi: 10.1016/0012-365X(92)00485-A.

[13] Z. Ryjáček, Matching extension in $K_{1,r}$-free graphs with independent claw centers, to appear in Discrete Math.

[14] W. T. Tutte, The factorization of linear graphs, J. London Math. Soc. 22 (1947) 107-111, doi: 10.1112/jlms/s1-22.2.107.

[15] W. W. Wong and C. K. Wong, Minimum k-Hamiltonian Graphs, J. Graph Theory 8 (1984) 155-165, doi: 10.1002/jgt.3190080118.