A degree condition for the existence of k‐factors with prescribed properties

Let k be an integer such that k≥3, and let G be a 2-connected graph of order n with n≥4k+1, kn even, and minimum degree at least k+1. We prove that if the maximum degree of each pair of nonadjacent vertices is at least n/2, then G has a k-factor excluding any given edge. The result of Nishimura (1992) is improved