DEGREE CONDITIONS AND FRACTIONAL k-FACTORS OF GRAPHS
Sizhong Zhou · Bulletin of the Korean Mathematical Society · 2011
Let k $\geq$ 1 be an integer, and let G be a 2-connected graph of order n with n $\geq$ max{7, 4k+1}, and the minimum degree $\delta(G)$ $\geq$ k+1. In this paper, it is proved that G has a fractional k-factor excluding any given edge if G satisfies max{ $d_G(x)$ , $d_G(y)$ } $\geq$ $\frac{n}{2}$ for each pair of nonadjacent vertices x, y of G. Furthermore, it is showed that the result in this paper is best possible in some sense.