Disproof of the List Hadwiger Conjecture

TL;DR

This paper disproves the List Hadwiger Conjecture by constructing specific graphs that are minor-free but not choosable within certain parameters, challenging previous assumptions in graph theory.

Contribution

It provides the first counterexamples to the conjecture, showing that not all $K_t$-minor-free graphs are $t$-choosable, thus refuting a long-standing hypothesis.

Findings

Constructed $K_{3t+2}$-minor-free graphs that are not $4t$-choosable

Disproved the List Hadwiger Conjecture for all $t \\geq 1$

Established new limitations on graph choosability related to minors.

Abstract

The List Hadwiger Conjecture asserts that every $K_t$-minor-free graph is $t$-choosable. We disprove this conjecture by constructing a $K_{3t+2}$-minor-free graph that is not $4t$-choosable for every integer $t\geq 1$.