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Smallest counterexample to the 5-flow conjecture has girth at least eleven. (English) Zbl 1211.05055

A graph admits a nowhere-zero k-flow if its edges can be oriented and assigned numbers so that for every vertex, the sum of the values on incoming edges equals the sum on the outgoing ones. The famous 5-flow conjecture of Tutte is that every bridgeless graph has a nowhere-zero 5-flow. The paper shows that a smallest counterexample to this conjecture must have girth at least 11.

MSC:

05C21 Flows in graphs
05C99 Graph theory
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References:

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