Presentations for Vertex Transitive Graphs
Combinatorics
2020-07-14 v1
Abstract
We generalise the standard constructions of a Cayley graph in terms of a group presentation by allowing some vertices to obey different relators than others. The resulting notion of presentation allows us to represent every vertex transitive graph. As an intermediate step, we prove that every countably infinite, connected, vertex transitive graph has a perfect matching. Incidentally, we construct an example of a 2-ended cubic vertex transitive graph which is not a Cayley graph, answering a question of Watkins from 1990.
Cite
@article{arxiv.2007.06432,
title = {Presentations for Vertex Transitive Graphs},
author = {Agelos Georgakopoulos and Matthias Hamann and Alex Wendland},
journal= {arXiv preprint arXiv:2007.06432},
year = {2020}
}
Comments
29 pages, 8 figures, main authors: Agelos Georgakopoulos and Alex Wendland, appendix by: Matthias Hamann and Alex Wendland