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Nowhere-zero 15-flow in 3-edge-connected bidirected graphs |
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| Authors: | Er Ling Wei Wen Liang Tang Dong Ye |
| Affiliation: | 1. Department of Mathematics, Renmin University of China, Beijing, 100872, P. R. China 2. Department of Mathematics, West Virginia University, Morgantown, WV, 26505, USA 3. Department of Mathematical Sciences, Middle Tennessee State University, Murfreesboro, TN, 37132, USA |
| Abstract: | It was conjectured by Bouchet that every bidirected graph which admits a nowhere-zero k flow will admit a nowhere-zero 6-flow. He proved that the conjecture is true when 6 is replaced by 216. Zyka improved the result with 6 replaced by 30. Xu and Zhang showed that the conjecture is true for 6-edge-connected graphs. And for 4-edge-connected graphs, Raspaud and Zhu proved it is true with 6 replaced by 4. In this paper, we show that Bouchet’s conjecture is true with 6 replaced by 15 for 3-edge-connected graphs. |
| Keywords: | Bidirected graph integer flow signed graph |
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