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Nowhere-zero 3-flows in products of graphs

✍ Scribed by Jinlong Shu; Cun-Quan Zhang

Publisher
John Wiley and Sons
Year
2005
Tongue
English
Weight
104 KB
Volume
50
Category
Article
ISSN
0364-9024

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✦ Synopsis

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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