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Comptes Rendus Mathématique
Volume 349, n° 19-20
pages 1021-1024 (novembre 2011)
Doi : 10.1016/j.crma.2011.08.007
Received : 25 May 2011 ;  accepted : 16 August 2011
Binding numbers and  -factors excluding a given k -factor
Nombre de liaisons et  -facteur excluant un k -facteur donné
 

Sizhong Zhou
School of Mathematics and Physics, Jiangsu University of Science and Technology, Mengxi Road 2, Zhenjiang, Jiangsu 212003, PR China 

Abstract

Let G be a graph of order n , and let   be nonnegative integers with  . An  -factor of G is defined as a spanning subgraph F of G such that   for each  . If  , then an  -factor is called a k -factor. In this Note, it is proved that if G has a k -factor Q ,  , the binding number  , and   for any nonempty independent subset X of  , then G has an  -factor F such that  .

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Résumé

Soit G un graphe dʼordre n et   des entiers positifs tels que  . Un  -facteur est défini comme étant un sous-graphe couvrant F de G tel que   pour tout  . Si  , alors un  -facteur est appelé k -facteur. Dans cette Note on démontre que si G a un k -facteur  , le nombre de liaisons   et   pour tout sous-ensemble X non vide indépendant de  , alors G a un  -facteur F tel que  .

The full text of this article is available in PDF format.

 This research was supported by Natural Science Foundation of the Higher Education Institutions of Jiangsu Province (10KJB110003) and Jiangsu University of Science and Technology (2010SL101J, 2009SL154J), and was sponsored by Qing Lan Project of Jiangsu Province.



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