Nowhere-zero Flows on Tensor Products of Signed Graphs

Let G1 and G2 be two signed connected graphs with δ(G1)≥2 and |E(G2)|≥2. In this paper, we prove that the tensor product of two such signed graphs admits a nowhere-zero 3-flow unless G2 is a tree with odd number of edges, in which case the tensor product admits a nowhere-zero 5-flow.