The Linear List Hadwiger Conjecture

Theorem 1.1: there is an absolute integer $C\ge1$ such that every finite nonempty simple graph satisfies $\chi_\ell(G)\le C\,h(G)$; Corollary 1.2 gives the ordinary linear Hadwiger bound $\chi(G)\le C\,h(G)$. The constant is not computed or optimised and must be at least $2$ by Steiner's examples. The proof shows $K_t$-minor-free graphs on at most $t^{11/10}$ vertices are $Lt$-choosable and then lifts this to all orders through Postle-style separability and a three-district recursion. It does not give $C$ close to $1$ or $2$.

Theorem 1.1: there is an absolute integer $C\ge1$ such that every finite nonempty simple graph satisfies $\chi_\ell(G)\le C\,h(G)$; Corollary 1.2 gives the ordinary linear Hadwiger bound $\chi(G)\le C\,h(G)$. The constant is not computed or optimised and must be at least $2$ by Steiner's examples. The proof shows $K_t$-minor-free graphs on at most $t^{11/10}$ vertices are $Lt$-choosable and then lifts this to all orders through Postle-style separability and a three-district recursion. It does not give $C$ close to $1$ or $2$.