A minimum degree condition of fractional $ (k,m)$-deleted graphs

Sizhong Zhou

doi:10.1016/j.crma.2009.09.022

Combinatorics

A minimum degree condition of fractional

(k, m)

-deleted graphs
[Une condition sur le degré minimal pour qu'un graphe soit

(k, m)

-effacé fractionnaire]

Présenté par : Jean-Yves Girard

Sizhong Zhou ¹

¹ School of Mathematics and Physics, Jiangsu University of Science and Technology, Mengxi Road 2, Zhenjiang, Jiangsu 212003, People's Republic of China

Comptes Rendus. Mathématique, Volume 347 (2009) no. 21-22, pp. 1223-1226.

Résumé
Abstract

Soit G un graphe d'ordre n et $k ⩾ 1$ , $m ⩾ 1$ deux entiers, nous notons $δ (G)$ le degré minimal de G. Dans cette Note nous montrons que si $n ⩾ 4 k - 5 + 2 (2 k + 1) m$ et $δ (G) ⩾ n / 2$ alors G est un graphe $(k, m)$ -effacé fractionnaire. De plus, nous montrons par un exemple que la condition sur le degré minimal ne peut être remplacée par $δ (G) ⩾ (n - 1) / 2$ .

Let G be a graph of order n, and let $k ⩾ 1$ and $m ⩾ 1$ be two integers. In this paper, we consider the relationship between the minimum degree $δ (G)$ and the fractional $(k, m)$ -deleted graphs. It is proved that if $n ⩾ 4 k - 5 + 2 (2 k + 1) m$ and $δ (G) ⩾ \frac{n}{2}$ , then G is a fractional $(k, m)$ -deleted graph. Furthermore, we show that the minimum degree condition is sharp in some sense.

Reçu le : 2008-10-10
Accepté le : 2009-09-14
Publié le : 2009-10-03

DOI : 10.1016/j.crma.2009.09.022

Affiliations des auteurs :

Sizhong Zhou ¹

¹ School of Mathematics and Physics, Jiangsu University of Science and Technology, Mengxi Road 2, Zhenjiang, Jiangsu 212003, People's Republic of China

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     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},
}

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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/

Bibliographie
Cité par

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[2] P. Katerinis Minimun degree of a graph and the existence of k-factors, Proc. Indian Acad. Sci. Math. Sci., Volume 94 (1985), pp. 123-127

[3] G. Liu; L. Zhang Fractional $(g, f)$ -factors of graphs, Acta Math. Sci., Volume 21B (2001) no. 4, pp. 541-545

[4] G. Liu; L. Zhang Toughness and the existence of fractional k-factors of graphs, Discrete Math., Volume 308 (2008), pp. 1741-1748

[5] J. Yu; G. Liu; M. Ma; B. Cao 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

Cité par Sources :

^☆ This research was supported by Jiangsu Provincial Educational Department (07KJD110048) and was sponsored by Qing Lan Project of Jiangsu Province.

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