On separators in K_h-minor-free graphs

This manuscript records possible improvements of the constants in Xinheng Lin’s arXiv preprint, “On separators in K_t-minor-free graphs” (arXiv:2610.40270, https://arxiv.org/abs/2610.40270).Building on the results of that preprint, the author used ChatGPT 6 Astra to develop the proposed improvements. In particular, this manuscript proposes a balanced vertex separator bound of min{ceil(n/3), 2.7278(h−1)√n} for every integer h ≥ 3 and every n-vertex K_h-minor-free graph, with further refinements and lower bounds discussed in the text.The proposed proof is substantially longer and more difficult to read than the original proof. The author has not personally checked this version of the manuscript; its review was carried out using GPT-6 Astra (Ultra). This manuscript is intended only to record the possibility of the stated improvements. The author does not intend to publish it in a formal journal.