Geodesic
Cycles in graphs with geometric property (T)
Jeroen Winkel1 orcid
1Westfälische Wilhelms-Universität Münster, Münster, Germany
Groups, geometry, and dynamics, Tome 18 (2024) no. 1, pp. 361-377

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DOI

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.
DOI : 10.4171/ggd/755
Classification : 05C38, 47L55, 51F30
Mots-clés : Geometric property (T), girth, cycles, Laplacian, combinatorial cost

Jeroen Winkel  1

1 Westfälische Wilhelms-Universität Münster, Münster, Germany 
Jeroen Winkel. Cycles in graphs with geometric property (T). Groups, geometry, and dynamics, Tome 18 (2024) no. 1, pp. 361-377. doi: 10.4171/ggd/755
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     title = {Cycles in graphs with geometric property {(T)}},
     journal = {Groups, geometry, and dynamics},
     pages = {361--377},
     year = {2024},
     volume = {18},
     number = {1},
     doi = {10.4171/ggd/755},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/755/}
}
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