Degree sum and nowhere-zero 3-flows

Let G be a simple graph on n vertices. In this paper, we prove that if G satisfies the condition that d(x) + d(y) >= n for each xy is an element of E(G), then G has no nowhere-zehro 3-flow if and only if G is either one of the five graphs on at most 6 vertices or one of a very special class of graphs on at least 6 vertices. (c) 2007 Elseiver B.V. All rights reserved.