Neighborhood conditions and fractional k-factors

Abstract. Let k be an integer such that k ≥ 1, and let G be a connected graph of order n such that n ≥ 9k − 1 − 4p2(k − 1)2 + 2, and the minimum degree δ(G) ≥ k. In this paper, it is proved that a graph G has a fractional k-factor if |NG(x) ∪ NG(y) | ≥ max{n/2, (n + k − 2)/2} for each pair of non-adjacent vertices x, y ∈ V (G)