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Flows in 3-edge-connected bidirected graphs |
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| Authors: | Erling Wei Wenliang Tang Xiaofeng Wang |
| Institution: | 1. Department of Mathematics, Renmin University of China, Beijing 100872, China; 2. Department of Mathematics, West Virginia University, Morgantown, WV 26505, USA; 3. Department of Mathematics and Actuarial Sciences, Indiana University Northwest, Gary, IN 46408, USA |
| 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. |
| Keywords: | Bidirected graph integer flow matroid |
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