Nowhere-zero 3-flows in Cayley graphs and Sylow 2-subgroups |
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Authors: | Mária Nánásiová Martin Škoviera |
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Affiliation: | (1) Department of Computer Science, Faculty of Mathematics, Physics and Informatics, Comenius University, 842 48 Bratislava, Slovakia |
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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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Keywords: | Nowhere-zero flow Cayley graph Group centre Sylow subgroup Nilpotent group |
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