A degree condition for the existence of connected [k, k + 1]-factors with prescribed properties

Abstract

Let G be a graph of order n ≥ 4k+8, where k is a positive integer with kn is even and δ(G) > k+1. We show that if max{dG(u),dG(v)} > n/2 for each pair of nonadjacent vertices u, v , then G has a connected [k, k + 1]-factor excluding any given edge e.