Expanders have a large girth Lipschitz spanning subgraphs

Gábor Kun

ELTE Budapest

Abstract

We show that every regular graph with good local expansion has a large girth Lipschitz spanning subgraph. This gives a finite analogue of the dynamical solution to the von Neumann problem by Gaboriau and Lyons. We reprove the Gaboriau-Lyons result and apply our theorem to the regular case of Thomassen's conjecture, too.