Abstract
A graph G is an odd-circuit tree if every block of G is an odd length circuit. It is proved in this paper that the product of every pair of graphs G and H admits a nowhere-zero 3-flow unless G is an odd-circuit tree and H has a bridge. This theorem is a partial result to the Tutte's 3-flow conjecture and generalizes a result by Imrich and Skrekovski [7] that the product of two bipartite graphs admits a nowhere-zero 3-flow. A byproduct of this theorem is that every bridgeless Cayley graph G = Cay(Γ,S) on an abelian group Γ with a minimal generating set S admits a nowhere-zero 3-flow except for odd prisms. © 2005 Wiley Periodicals, Inc. J Graph Theory
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