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Nowhere-zero 3-flows in Cayley graphs and Sylow 2-subgroups. (English) Zbl 1208.05053

Summary: Tutte’s 3-Flow Conjecture suggests that every bridgeless graph with no 3-edge-cut can have its edges directed and labelled by the numbers 1 or 2 in such a way that at each vertex the sum of incoming values equals the sum of outgoing values. In this paper we show that Tutte’s 3-Flow Conjecture is true for Cayley graphs of groups whose Sylow 2-subgroup is a direct factor of the group; in particular, it is true for Cayley graphs of nilpotent groups. This improves a recent result of P.Potočnik, M. Škoviera and P. Škrekovski [Discrete Math. 297,119-127 (2005)] concerning nowhere-zero 3-flows in abelian Cayley graphs.

MSC:

05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
20D20 Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure
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