%0 Journal Article
%T Toughness and the Existence of Fractional 3-Factor
%A Yun Gao
%A Yungang Zhang
%A Wei Gao
%J Advances in Mathematical and Computational Methods
%D 2012
%I 
%R 10.5729
%X Let G be a graph, a variation of Toughness is defined as ¦Ó (G) =min{ ( ) 1G¦Ø G  S   ,S V(G), ¦Ø(G  S) ¡Ý 2} if G is not complete, and ¦Ó (G) =¡Þ if G is complete. One conjectureconcern toughness and exist of fractional k-factor is that: Let G be a graph, if ¦Ó (G)>k for integerk ¡Ý 2, then G has fractional k-factor. This conjecute has proof true for k=2. In this paper, we provethat G has fraction 3-factor if ¦Ó (G) >3.
%K Graph
%K Fractional factor
%K Toughness.
%U http://www.ier-institute.org/2160-0635/v2/no1/063.pdf