We prove that in a certain statistical sense the Cayley graph of almost every
finitely presented group with $m\ge 2$ generators contains a subdivision of the complete graph on
$l\le 2m+1$ vertices. In particular, this Cayley graph is non planar. We also show that some group
constructions preserve the planarity.
Publié le : 2004-12-14
Classification:
Cayley graph,
small cancellation groups,
generic properties of groups,
05C25,
20F06,
20P05
@article{1102689123,
author = {Arzhantseva, G. N. and Cherix, P.-A.},
title = {On the Cayley graph of a generic finitely presented group},
journal = {Bull. Belg. Math. Soc. Simon Stevin},
volume = {11},
number = {1},
year = {2004},
pages = { 589-601},
language = {en},
url = {http://dml.mathdoc.fr/item/1102689123}
}
Arzhantseva, G. N.; Cherix, P.-A. On the Cayley graph of a generic finitely presented group. Bull. Belg. Math. Soc. Simon Stevin, Tome 11 (2004) no. 1, pp. 589-601. http://gdmltest.u-ga.fr/item/1102689123/