Nowhere-zero 5-flows and (1, 2)-factors

A graph G has a nowhere-zero k-flow if there exists an orientation D of the edges and an integer flow ϕ such that for all e ∈ D ( G ) , 0 < | ϕ ( 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.