Neighborhood Conditions and Fractional k-Factors
Malaysian Mathematical, Sizhong Zhou, Hongxia Liu · 2009
Let k be an integer such that k 1, and let G be a connected graph of order n such that n 9k 1 4 2(k 1)2 + 2, and the minimum degree (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 2 V (G).