A degree condition for the existence of k‐factors with prescribed properties
Changping Wang · International Journal of Mathematics and Mathematical Sciences · 2005
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.