Year: 2026
Type: preprint
Abstract: Delcourt and Postle proved that every $K_t$-minor-free graph is $O(t\log\log t)$-colorable and reduced the Linear Hadwiger Conjecture to coloring $K_t$-minor-free graphs on $O(t\log^4 t)$ vertices. In this paper, we use the star contraction technique to improve their bound for small graphs and use their reduction to extend this improvement to all $K_t$-minor-free graphs. Thus we improve their $O(t\log\log t)$ bound to $O(t\sqrt{\log\log t})$.
Source: arXiv (Cornell University)
Author: Lin, Xinheng
Institution: Fuzhou University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212055661