ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

Discussiones Mathematicae Graph Theory

IMPACT FACTOR 2018: 0.741

SCImago Journal Rank (SJR) 2018: 0.763

Rejection Rate (2018-2019): c. 84%

Discussiones Mathematicae Graph Theory


Discussiones Mathematicae Graph Theory 16(1) (1996) 41-51
DOI: 10.7151/dmgt.1022


Odile Favaron

LRI, Bât. 490, Université de Paris-Sud
91405 Orsay cedex, France


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.

1991 Mathematics Subject Classification: 05C70.


[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 K1,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.