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Paper   IPM / M / 11198
School of Mathematics
  Title:   On zero-sum 6-flows of graphs
1.  S. Akbari
2.  N. Ghareghani
3.  G. B. Khosrovshahi (Joint with A. Mahmoody)
  Status:   Published
  Journal: Linear Algebra Appl.
  Vol.:  430
  Year:  2009
  Pages:   3047-3052
  Supported by:  IPM
For a graph G, a zero-sum k-flow 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 zero-sum flow for a given graph and they prove that every 2-edge connected bipartite graph has a zero-sum 6-flow, every cubic graph has a zero-sum 5-flow and every regular graph of even degree has a zero-sum 3-flow. The authors further conjecture that every graph which has a zero-sum flow, has a zero-sum 6-flow; this conjecture is implied by the Bouchet conjecture.

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