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.

Abstract (VO)
Résumé

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.

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 $δ (G) ⩾ (n - 1) / 2$ .

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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     title = {A minimum degree condition of fractional $ (k,m)$-deleted graphs},
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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/

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Wei Gao; Wei-fan Wang; Yao-jun Chen Sharp isolated toughness bound for fractional $(k, m)$ -deleted graphs, Acta Mathematicae Applicatae Sinica. English Series, Volume 41 (2025) no. 1, pp. 252-269 | DOI:10.1007/s10255-024-1067-x | Zbl:7965932
Wei Gao; Juan Luis García Guirao; Mahmoud Abdel-Aty; Wenfei Xi An independent set degree condition for fractional critical deleted graphs, Discrete and Continuous Dynamical Systems. Series S, Volume 12 (2019) no. 4-5, pp. 877-886 | DOI:10.3934/dcdss.2019058 | Zbl:1418.05101
Sizhong Zhou; Lan Xu; Yang Xu A sufficient condition for the existence of a $k$ -factor excluding a given $r$ -factor, Applied Mathematics and Nonlinear Sciences, Volume 2 (2017) no. 1, pp. 13-20 | DOI:10.21042/amns.2017.1.00002 | Zbl:1375.05222
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Wei Gao; Li Liang; Tianwei Xu; Juxiang Zhou Degree conditions for fractional $(g, f, n^{'}, m)$ -critical deleted graphs and fractional ID- $(g, n, f, m)$ -deleted graphs, Bulletin of the Malaysian Mathematical Sciences Society. Second Series, Volume 39 (2016), p. s315-s330 | DOI:10.1007/s40840-015-0194-1 | Zbl:1339.05308
Si Zhong Zhou Binding numbers for fractional ID- $k$ -factor-critical graphs, Acta Mathematica Sinica. English Series, Volume 30 (2014) no. 1, pp. 181-186 | DOI:10.1007/s10114-013-1396-9 | Zbl:1287.05124
Sizhong Zhou; Zhiren Sun; Hui Ye A toughness condition for fractional -deleted graphs, Information Processing Letters, Volume 113 (2013) no. 8, p. 255 | DOI:10.1016/j.ipl.2013.01.021
Sizhong Zhou A new neighborhood condition for graphs to be fractional $(k, m)$ -deleted graphs, Applied Mathematics Letters, Volume 25 (2012) no. 3, pp. 509-513 | DOI:10.1016/j.aml.2011.09.048 | Zbl:1243.05204
Sizhong Zhou; Zhiren Sun; Hongxia Liu A minimum degree condition for fractional ID- $[a, b]$ -factor-critical graphs, Bulletin of the Australian Mathematical Society, Volume 86 (2012) no. 2, pp. 177-183 | DOI:10.1017/s0004972711003467 | Zbl:1252.05182
Sizhong Zhou Some new sufficient conditions for graphs to have fractional $k$ -factors, International Journal of Computer Mathematics, Volume 88 (2011) no. 3, pp. 484-490 | DOI:10.1080/00207161003681286 | Zbl:1230.05243
Sizhong Zhou A neighbourhood condition for graphs to be fractional $(k, m)$ -deleted graphs, Glasgow Mathematical Journal, Volume 52 (2010) no. 1, pp. 33-40 | DOI:10.1017/s0017089509990139 | Zbl:1260.05124

Cité par 11 documents. Sources : Crossref, zbMATH

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

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