On the limit of large girth graph sequences

TL;DR

This paper proves that any involution-invariant measure on trees with bounded degree can be realized as the local limit of large girth graph sequences, answering a question in graph theory.

Contribution

It establishes a correspondence between involution-invariant measures and large girth graph sequences, advancing understanding of local limits in graph theory.

Findings

Any involution-invariant measure on bounded degree trees arises as a local limit.

The result answers a previously open question by Bollobás and Riordan.

Provides a characterization of limits of large girth graphs.

Abstract

We prove that any involution-invariant probability measure on the space of trees with maximum degrees at most d arises as the local limit of a convergent large girth graph sequence. This answers a question of Bollobas and Riordan.