Abstract
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 Potočnik et al. (Discrete Math. 297:119–127, 2005) concerning nowhere-zero 3-flows in abelian Cayley graphs.
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Nánásiová, M., Škoviera, M. Nowhere-zero 3-flows in Cayley graphs and Sylow 2-subgroups. J Algebr Comb 30, 103–111 (2009). https://doi.org/10.1007/s10801-008-0153-0
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DOI: https://doi.org/10.1007/s10801-008-0153-0