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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1054, author = {Odile Favaron and Evelyne Favaron and Zden\u ek Ryj\'a\v cek}, title = {Factor-criticality and matching extension in DCT-graphs}, journal = {Discussiones Mathematicae Graph Theory}, volume = {17}, year = {1997}, pages = {271-278}, zbl = {0907.05040}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1054} }
Odile Favaron; Evelyne Favaron; Zdenĕk Ryjáček. Factor-criticality and matching extension in DCT-graphs. Discussiones Mathematicae Graph Theory, Tome 17 (1997) pp. 271-278. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1054/
[000] [1] A. Ainouche, Quasi claw-free graphs. Preprint, submitted. | Zbl 0888.05038
[001] [2] A. Ainouche, O. Favaron and H. Li, Global insertion and hamiltonicity in DCT-graphs, Discrete Math. (to appear). | Zbl 0958.05084
[002] [3] J.A. Bondy and U.S.R. Murty, Graph Theory with Applications (Macmillan, London and Elsevier, New York, 1976). | Zbl 1226.05083
[003] [4] O. Favaron, Stabilité, domination, irredondance et autres parametres de graphes (These d'Etat, Université de Paris-Sud, 1986).
[004] [5] M. Las Vergnas, A note on matching in graphs, Cahiers Centre Etudes Rech. Opér. 17 (1975) 257-260.
[005] [6] M.D. Plummer, On n-extendable graphs, Discrete Math. 31 (1980) 201-210, doi: 10.1016/0012-365X(80)90037-0.
[006] [7] M.D. Plummer, Extending matchings in claw-free graphs, Discrete Math. 125 (1994) 301-308, doi: 10.1016/0012-365X(94)90171-6.
[007] [8] M.D. Plummer, Extending matchings in graphs: A survey, Discrete Math. 127 (1994) 277-292, doi: 10.1016/0012-365X(92)00485-A.
[008] [9] Z. Ryjácek, Almost claw-free graphs, J. Graph Theory 18 (1994) 469-477, doi: 10.1002/jgt.3190180505. | Zbl 0808.05067
[009] [10] Z. Ryjácek, Matching extension in -free graphs with independent claw centers, Discrete Math. 164 (1997) 257-263, doi: 10.1016/S0012-365X(96)00059-3. | Zbl 0872.05044
[010] [11] D.P. Sumner, Graphs with 1-factors, Proc. Amer. Math. Soc. 42 (1974) 8-12. | Zbl 0293.05157
[011] [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. | Zbl 0338.05118