Cycles in graphs with geometric property (T)
Jeroen Winkel
Westfälische Wilhelms-Universität Münster, Münster, Germany
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Abstract
We show that a sequence of graphs with uniformly bounded vertex degrees, number of vertices going to infinity, and with geometric property (T) has many small cycles. We also show that when a small part of such a sequence of graphs with geometric property (T) is changed, it still has geometric property (T), provided that it is still an expander. We use this to give an example of a sequence of graphs with geometric property (T) that has large cycle-free balls.
Cite this article
Jeroen Winkel, Cycles in graphs with geometric property (T). Groups Geom. Dyn. 18 (2024), no. 1, pp. 361–377
DOI 10.4171/GGD/755