A degree condition for a graph to have (a, b)-parity factors

Let a and b be two positive integers such that a <= b and a equivalent to b (mod 2). A graph F is an (a, b)-parity factor of a graph G if F is a spanning subgraph of G and for all vertices v is an element of V(F), d(F)(v) equivalent to b (mod 2) and a <= d(p)(v) <= b. In this paper we prove that every connected graph G with n >= b(a + b)(a + b + 2)/(2a) vertices has an (a, b)-parity factor if na is even, delta(G) >= (b a)/a + a, and for any two nonadjacent vertices u, v is an element of V(G), max{dG(u), delta G(v)} >= an/a+b This extends an earlier result of Nishimura (1992) and strengthens a result of Cai and Li (1998). (C) 2017 Elsevier B.V. All rights reserved.