On the size of spheres of relations with a transitive group of automorphisms
| dc.creator | Hamidoune, Yahya Ould | |
| dc.date | 2006-03-21 | |
| dc.date.accessioned | 2026-07-07T07:07:07Z | |
| dc.date.available | 2026-07-07T07:07:07Z | |
| dc.description | Let $Γ=(V,E)$ be a point-transitive reflexive relation. Let $v\in V$ and put $r=|Γ(v)|.$ Also assume $Γ^j(v)\cap Γ^{-}(v)=\{v\}$. Then $$ |Γ^{j} (v)\setminus Γ^{j-1} (v)| \ge r-1.$$ In particular we have $ |Γ^{j} (v)| \ge 1+(r-1)j.$ The last result confirms a recent conjecture of Seymour in the case vertex-transitive graphs. Also it gives a short proof for the validity of the Caccetta-Häggkvist conjecture for vertex-transitive graphs and generalizes an additive result of Shepherdson. | |
| dc.identifier | https://arxiv.org/abs/math/0603504 | |
| dc.identifier | http://arxiv.org/abs/math/0603504 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/110275 | |
| dc.subject | Combinatorics | |
| dc.subject | 20D60 | |
| dc.title | On the size of spheres of relations with a transitive group of automorphisms | |
| dc.type | text |