A proof of the Alon–Seymour–Thomas conjecture

This manuscript presents a proof of the Alon–Seymour–Thomas conjecture developed under the author’s guidance using ChatGPT 6pro. Codex was used to prepare the initial draft. The author has carried out a preliminary verification of the proof, and further refinement of the manuscript is in progress.More precisely, for every integer h ≥ 3, every n-vertex K_h-minor-free graph has a vertex set of size at most min{n, 21h√n} whose deletion leaves every component with at most 2n/3 vertices.The main ingredient is a connected hitting set theorem obtained by combining vertex expansion with finite optimal transport.