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The number of nowhere-zero flows on graphs and signed graphs
2006
Journal of combinatorial theory. Series B (Print)
A nowhere-zero k-flow on a graph Γ is a mapping from the edges of Γ to the set {±1, ±2, . . . , ±(k − 1)} ⊂ Z such that, in any fixed orientation of Γ , at each node the sum of the labels over the edges pointing towards the node equals the sum over the edges pointing away from the node. We show that the existence of an integral flow polynomial that counts nowhere-zero k-flows on a graph, due to Kochol, is a consequence of a general theory of inside-out polytopes. The same holds for flows on
doi:10.1016/j.jctb.2006.02.011
fatcat:kl32sgkx4vbj5hmjzaikv25k24