DEGREE CONDITIONS AND FRACTIONAL k-FACTORS OF GRAPHS

Let k >= I be an integer, and let G be a 2-connected graph of order n with n >= max{7, 4k + 1}, and the minimum degree delta(G) >= 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)} >= n/2 for each pair of nonadjacent vertices x,p of C. Furthermore, it is showed that the result in this paper is best possible in some sense.