Discussiones Mathematicae Graph Theory  17(2) (1997)  271-278
doi: 10.7151/dmgt.1054

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Odile Favaron

Evelyne Flandrin

L.R.I., URA 410 C.N.R.S. Bât. 490, Université de Paris-Sud
91405-Orsay cedex, France

Zdenk Ryjáek

Department of Mathematics, University of West Bohemia
Univerzitní 22, 306 14 Plze, Czech Republic


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.

1991 Mathematics Subject Classification: 05C70.


[1] A. Ainouche, Quasi claw-free graphs. Preprint, submitted.
[2] A. Ainouche, O. Favaron and H. Li, Global insertion and hamiltonicity in DCT-graphs, Discrete Math. (to appear).
[3] J.A. Bondy and U.S.R. Murty, Graph Theory with Applications (Macmillan, London and Elsevier, New York, 1976).
[4] O. Favaron, Stabilité, domination, irredondance et autres parametres de graphes (These d'Etat, Université de Paris-Sud, 1986).
[5] M. Las Vergnas, A note on matching in graphs, Cahiers Centre Etudes Rech. Opér. 17 (1975) 257-260.
[6] M.D. Plummer, On n-extendable graphs, Discrete Math. 31 (1980) 201-210, doi: 10.1016/0012-365X(80)90037-0.
[7] M.D. Plummer, Extending matchings in claw-free graphs, Discrete Math. 125 (1994) 301-308, doi: 10.1016/0012-365X(94)90171-6.
[8] M.D. Plummer, Extending matchings in graphs: A survey, Discrete Math. 127 (1994) 277-292, doi: 10.1016/0012-365X(92)00485-A.
[9] Z. Ryjácek, Almost claw-free graphs, J. Graph Theory 18 (1994) 469-477, doi: 10.1002/jgt.3190180505.
[10] Z. Ryjácek, Matching extension in K1,r-free graphs with independent claw centers, Discrete Math. 164 (1997) 257-263, doi: 10.1016/S0012-365X(96)00059-3.
[11] D.P. Sumner, Graphs with 1-factors, Proc. Amer. Math. Soc. 42 (1974) 8-12.
[12] D.P. Sumner, 1-factors and antifactor sets, J. London Math. Soc. 13 (2) (1976) 351-359, doi: 10.1112/jlms/s2-13.2.351.