Large complete minors in expanding graphs

TL;DR

This paper extends previous work on large complete minors in expanding graphs by exploring the relationship between the existence of such minors and vertex expansion properties, providing new insights into graph structure.

Contribution

It introduces a novel connection between large complete minors and vertex expansion in graphs, extending prior results on super-constant expansion factors.

Findings

Established a link between large minors and vertex expansion.

Extended previous results to broader classes of graphs.

Provided theoretical bounds relating minors and expansion properties.

Abstract

In 2009, Krivelevich and Sudakov studied the existence of large complete minors in $(t,\alpha)$-expanding graphs whenever the expansion factor $t$ becomes super-constant. In this paper, we give an extension of the results of Krivelevich and Sudakov by investigating a connection between the existence of large complete minors in graphs and good vertex expansion properties.