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Flows in 3-edge-connected bidirected graphs

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Abstract

It was conjectured by A. Bouchet that every bidirected graph which admits a nowhere-zero k-flow admits a nowhere-zero 6-flow. He proved that the conjecture is true when 6 is replaced by 216. O. Zyka improved the result with 6 replaced by 30. R. Xu and C. Q. Zhang showed that the conjecture is true for 6-edge-connected graph, which is further improved by A. Raspaud and X. Zhu for 4-edge-connected graphs. The main result of this paper improves Zyka’s theorem by showing the existence of a nowhere-zero 25-flow for all 3-edge-connected graphs.

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Authors and Affiliations

  1. Department of Mathematics, Renmin University of China, Beijing, 100872, China

    Erling Wei

  2. Department of Mathematics, West Virginia University, Morgantown, WV, 26505, USA

    Wenliang Tang

  3. Department of Mathematics and Actuarial Sciences, Indiana University Northwest, Gary, IN, 46408, USA

    Xiaofeng Wang

Authors
  1. Erling Wei
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  2. Wenliang Tang
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  3. Xiaofeng Wang
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Correspondence to Erling Wei.

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Wei, E., Tang, W. & Wang, X. Flows in 3-edge-connected bidirected graphs. Front. Math. China 6, 339–348 (2011). https://doi.org/10.1007/s11464-011-0111-3

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  • DOI: https://doi.org/10.1007/s11464-011-0111-3

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