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Zero-sum flows in regular graphs

Akbari, S ; Sharif University of Technology | 2010

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  1. Type of Document: Article
  2. DOI: 10.1007/s00373-010-0946-5
  3. Publisher: 2010
  4. Abstract:
  5. For an undirected graph G, a zero-sum flow is an assignment of non-zero real numbers to the edges, such that the sum of the values of all edges incident with each vertex is zero. It has been conjectured that if a graph G has a zero-sum flow, then it has a zero-sum 6-flow. We prove this conjecture and Bouchet's Conjecture for bidirected graphs are equivalent. Among other results it is shown that if G is an r-regular graph (r ≥ 3), then G has a zero-sum 7-flow. Furthermore, if r is divisible by 3, then G has a zero-sum 5-flow. We also show a graph of order n with a zero-sum flow has a zero-sum (n + 3)2-flow. Finally, the existence of k-flows for small graphs is investigated
  6. Keywords:
  7. Bidirected graph ; Regular graph ; Zero-sum flow
  8. Source: Graphs and Combinatorics ; Volume 26, Issue 5 , 2010 , Pages 603-615 ; 09110119 (ISSN)
  9. URL: http://link.springer.com/article/10.1007%2Fs00373-010-0946-5