Hadwiger's conjecture: finite vs infinite graphs

TL;DR

This paper explores various forms of Hadwiger's conjecture, comparing its validity and implications for both finite and infinite graphs, aiming to deepen understanding of graph minors and chromatic properties.

Contribution

It introduces and analyzes different versions of Hadwiger's conjecture applicable to finite and infinite graphs, highlighting their differences and potential implications.

Findings

Identifies key differences between finite and infinite graph cases

Proposes new variants of Hadwiger's conjecture for infinite graphs

Provides insights into graph minor and chromatic number relationships

Abstract

We study some versions of the statement of Hadwiger's conjecture for finite as well as infinite graphs.