Large expander subgraphs in high genus triangulations

TL;DR

This paper demonstrates that high genus random triangulations contain large expander subgraphs, providing new criteria for identifying large expanders in arbitrary graphs.

Contribution

It introduces novel criteria for the existence of large expander subgraphs and applies them to high genus triangulations, answering a previously open question.

Findings

High genus triangulations contain large expander subgraphs

New general criteria for large expanders in arbitrary graphs

Addresses a question posed by Benjamini

Abstract

We prove that random triangulations of high genus contain very large expander subgraphs, answering a question of Benjamini. Our approach relies on new general criteria for arbitrary graphs to contain large expander subgraphs.