Abstract

A graph G has a nowhere-zero k-flow if there exists an orientation D of the edges and an integer flow φ{symbol} such that for all e ∈ D (G), 0 < | φ{symbol} (e) | < k. A (1, 2)-factor is a subset of the edges F ⊆ E (G) such that the degree of any vertex in the subgraph induced by F is 1 or 2. It is known that cubic graphs having a nowhere-zero k-flow with k = 3, 4 are characterized by properties of the cycles of the graph. We extend these results by giving a characterization of cubic graphs having a nowhere-zero 5-flow based on the existence of a (1, 2)-factor of the graph such that the cycles of the graph satisfies an algebraic property. © 2008 Elsevier B.V. All rights reserved.