A neighborhood union condition for fractional (k, m)-deleted graphs

A graph G is called a fractional (k, m)-deleted graph if any in edges are removed from G then the resulting graph admits a fractional k-factor. In this paper, we prove that for integers k >= 2, m >= 0, n >= 8k + 4m - 7, and delta(G) >= k + m, if vertical bar N-G(x) boolean OR N-G(y)vertical bar >= n/2 for each pair of non-adjacent vertices x, y of G, then G is a fractional (k, m)-deleted graph. The bounds for neighborhood union condition, order and the minimum degree of G are all sharp.