科研之友
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摘要
Let G a graph of order n, and k >= 1 an integer. Let h: E(G) -> [0,1] be a function. If Sigma(e epsilon x)h(e) = k holds for each x is an element of V(G), we call G[F-h] a fractional k-factor of G with indicator functional h where F-h = {e is an element of E(G) : h(e) > 0}. In this paper, it is proved that G has a fractional k-factor including any given edge if G satisfies n >= 4k - 3, delta(G) >= k and and d(G)(x)+d(G)(y) >= n+ 1 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.
