Year: 2026
Type: preprint
Abstract: The linear list Hadwiger conjecture asserts that every $K_t$-minor-free graph is $O(t)$-choosable. Following an approach outlined by Delcourt and Postle, we recently established $O(t\log\log t)$-choosability. Soon afterward, OpenAI provided a proof of the conjecture. A key new ingredient of their proof is a linear bound on the choice number of $K_t$-minor-free graphs with at most $t^{11/10}$ vertices. In this paper, we give a relatively simple proof of this small-graph bound for graphs with at most $t(\ln t)^5$ vertices.Combining this with the argument from our earlier $O(t\log\log t)$ bound, we obtain a shorter and somewhat more accessible proof of the conjecture.
Source: arXiv (Cornell University)
Authors: Gu, Yangyan, Xu, Rongxing
Institutions: Shaoxing University, Zhejiang Normal University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Award: G4788007701
OpenAlex ID: W7216493245