Presentations for Vertex Transitive Graphs

Autor:	Georgakopoulos, Agelos, Hamann, Matthias, Wendland, Alex
Rok vydání:	2020
Předmět:	Mathematics - Combinatorics 05E18 (primary) 05E16 20A99 (secondary) F.2.2
Druh dokumentu:	Working Paper
Popis:	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. Comment: 29 pages, 8 figures, main authors: Agelos Georgakopoulos and Alex Wendland, appendix by: Matthias Hamann and Alex Wendland
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2007.06432 Zobrazit plný text záznamu View this record from Arxiv