Nowhere-zero 15-Flow in 3-Edge-connected Bidirected Graphs  

作　　者：Er Ling WEI Wen Liang TANG Dong YE 

机构地区：[1]Department of Mathematics,Renmin University of China [2]Department of Mathematics,West Virginia University [3]Department of Mathematical Sciences,Middle Tennessee State University

出　　处：《Acta Mathematica Sinica,English Series》2014年第4期649-660,共12页数学学报（英文版）

基　　金：Supported by the Fundamental Research Funds for the Central Universities;the Research Funds of Renmin University of China Project(Grant No.10XNB054)

摘　　要：It was conjectured by Bouchet that every bidirected graph which admits a nowhere-zero κ 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.It was conjectured by Bouchet that every bidirected graph which admits a nowhere-zero κ 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.

关 键 词：Bidirected graph integer flow signed graph 

分 类 号：O157.5[理学—数学] TP391.41[理学—基础数学]