The size of graphs without nowhere-zero 4-flows

Let G be a 2-edge-connected simple graph with order n. We show that if | V(G)| ≤ 17, then either G has a nowhere-zero 4-flow, or G is contractible to the Petersen graph. We also show that for n large, if | V(G)| n ? 17/2 + 34, then either G has a nonwhere-zero 4-flow, or G can be contracted to the Petersen graph. © 1995 John Wiley & Sons, Inc.