```	%0 Journal Article
%A Sizhong Zhou and  Hongxia Liu
%D 2011
%J International Journal of Mathematical and Computational Sciences
%B World Academy of Science, Engineering and Technology
%I Open Science Index 55, 2011
%T On Fractional (k,m)-Deleted Graphs with Constrains Conditions
%U https://publications.waset.org/pdf/3345
%V 55
%X Let G be a graph of order n, and let k  2 and m  0 be two integers. Let h : E(G)  [0, 1] be a function. If e&ni;x h(e) = k holds for each x  V (G), then we call G[Fh] a fractional k-factor of G with indicator function h where Fh = {e  E(G) : h(e) &gt; 0}. A graph G is called a fractional (k,m)-deleted graph if there exists a fractional k-factor G[Fh] of G with indicator function h such that h(e) = 0 for any e  E(H), where H is any subgraph of G with m edges. In this paper, it is proved that G is a fractional (k,m)-deleted graph if (G)  k + m + m k+1 , n  4k2 + 2k &minus; 6 + (4k 2 +6k&minus;2)m&minus;2 k&minus;1 and max{dG(x), dG(y)}  n 2 for any vertices x and y of G with dG(x, y) = 2. Furthermore, it is shown that the result in this paper is best possible in some sense.

%P 1081 - 1083
```