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arXiv · 1403.2322

Multi-way expanders and imprimitive group actions on graphs

Masato Mimura
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Abstract

For n at least 2, the concept of n-way expanders was defined by various researchers. Bigger n gives a weaker notion in general, and 2-way expanders coincide with expanders in usual sense. Koji Fujiwara asked whether these concepts are equivalent to that of ordinary expanders for all n for a sequence of Cayley graphs. In this paper, we answer his question in the affirmative. Furthermore, we obtain universal inequalities on multi-way isoperimetric constants on any finite connected vertex-transitive graph, and show that gaps between these constants imply the imprimitivity of the group action on the graph.

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Masato Mimura. 2015-06-25. Multi-way expanders and imprimitive group actions on graphs. https://doi.org/10.1093/imrn%2Frnv220

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