Flows in 3-edge-connected bidirected graphs

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 f...

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Bibliographic Details
Published in:Frontiers of mathematics in China 2011-04, Vol.6 (2), p.339-348
Main Authors: WEI, Erling, TANG, Wenliang, WANG, Xiaofeng
Format: Article
Language:English
Subjects:
Bidirected graph
China
Circuits
Existence theorems
Graph theory
Graphs
integer flow
Mathematical analysis
Mathematics
Mathematics and Statistics
matroid
Research Article
Studies
Theorems
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Summary: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.
ISSN:1673-3452
1673-3576
DOI:10.1007/s11464-011-0111-3