[Une condition sur le degré minimal pour qu'un graphe soit -effacé fractionnaire]
Soit G un graphe d'ordre n et , deux entiers, nous notons le degré minimal de G. Dans cette Note nous montrons que si et alors G est un graphe -effacé fractionnaire. De plus, nous montrons par un exemple que la condition sur le degré minimal ne peut être remplacée par .
Let G be a graph of order n, and let and be two integers. In this paper, we consider the relationship between the minimum degree and the fractional -deleted graphs. It is proved that if and , then G is a fractional -deleted graph. Furthermore, we show that the minimum degree condition is sharp in some sense.
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Sizhong Zhou 1
@article{CRMATH_2009__347_21-22_1223_0, author = {Sizhong Zhou}, title = {A minimum degree condition of fractional $ (k,m)$-deleted graphs}, journal = {Comptes Rendus. Math\'ematique}, pages = {1223--1226}, publisher = {Elsevier}, volume = {347}, number = {21-22}, year = {2009}, doi = {10.1016/j.crma.2009.09.022}, language = {en}, }
Sizhong Zhou. A minimum degree condition of fractional $ (k,m)$-deleted graphs. Comptes Rendus. Mathématique, Volume 347 (2009) no. 21-22, pp. 1223-1226. doi : 10.1016/j.crma.2009.09.022. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.09.022/
[1] Graph Theory with Applications, The Macmillan Press, London, 1976
[2] Minimun degree of a graph and the existence of k-factors, Proc. Indian Acad. Sci. Math. Sci., Volume 94 (1985), pp. 123-127
[3] Fractional -factors of graphs, Acta Math. Sci., Volume 21B (2001) no. 4, pp. 541-545
[4] Toughness and the existence of fractional k-factors of graphs, Discrete Math., Volume 308 (2008), pp. 1741-1748
[5] A degree condition for graphs to have fractional factors, Adv. Math. (China), Volume 35 (2006) no. 5, pp. 621-628
[6] S. Zhou, Z. Duan, Binding number and fractional k-factors of graphs, Ars Combin., in press
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☆ This research was supported by Jiangsu Provincial Educational Department (07KJD110048) and was sponsored by Qing Lan Project of Jiangsu Province.
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