Comptes Rendus
no. 21-22
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 Zhou1
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.

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⩾4k−5+2(2k+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⩾4k−5+2(2k+1)m and δ(G)⩾n2, then G is a fractional (k,m)-deleted graph. Furthermore, we show that the minimum degree condition is sharp in some sense.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2009.09.022

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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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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[6] S. Zhou, Z. Duan, Binding number and fractional k-factors of graphs, Ars Combin., in press

  • 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, p. 252 | DOI:10.1007/s10255-024-1067-x
  • 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, p. 13 | DOI:10.21042/amns.2017.1.00002
  • Wei Gao; Li Liang; Tianwei Xu; Juxiang Zhou Degree Conditions for Fractional (g,f,n′,m) ( g , f , n ′ , m ) -Critical Deleted Graphs and Fractional ID-(g, f, m)-Deleted Graphs, Bulletin of the Malaysian Mathematical Sciences Society, Volume 39 (2016) no. S1, p. 315 | DOI:10.1007/s40840-015-0194-1
  • Si Zhong Zhou Binding numbers for fractional ID-k-factor-critical graphs, Acta Mathematica Sinica, English Series, Volume 30 (2014) no. 1, p. 181 | DOI:10.1007/s10114-013-1396-9
  • 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, p. 509 | DOI:10.1016/j.aml.2011.09.048
  • 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, p. 177 | DOI:10.1017/s0004972711003467
  • Sizhong Zhou Some new sufficient conditions for graphs to have fractionalk-factors, International Journal of Computer Mathematics, Volume 88 (2011) no. 3, p. 484 | DOI:10.1080/00207161003681286

Cité par 8 documents. Sources : Crossref

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

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