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Paper IPM / M / 11198  


Abstract:  
For a graph G, a zerosum kflow is an assignment of labels from the set {±1, ±2,..., ±(k−1)} to the edges of G such that the total sum of all edges incident with any vertex of G is zero.
The authors give a necessary and sufficient condition for the existence of a zerosum flow for a given graph and they prove that every 2edge connected bipartite graph has a zerosum 6flow, every cubic graph has a zerosum 5flow and every regular graph of even degree has a zerosum 3flow. The authors further conjecture that every graph which has a zerosum flow, has a zerosum 6flow; this conjecture is implied by the Bouchet conjecture.
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