# Noon lecture

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On 14.3.2013 at 12:20 in S6, there is the following noon lecture:

# 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.

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