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On separators in Kt-minor-free graphs
Abstract
This manuscript presents a proof of the Alon--Seymour--Thomas conjecture developed under the author's guidance using ChatGPT 6pro. The author has checked every formula and theorem by hand and used Codex to assist with writing. GPT 6.1 Sol (Max) was also used to check the proof repeatedly and to generate numerous examples for verification. More precisely, for every integer h≥3, every n-vertex Kh-minor-free graph has a vertex set of size at most minn,21h√n whose deletion leaves every component with at most 2n/3 vertices.
Related
- Kh-Minor-Free Graphs Have Balanced Separators of Size O(h√n)
- Revisiting separators in string graphs, region intersection graphs, and induced-minor-free graphs
- Coloring Small Kt-Minor-Free Graphs
- A note on highly connected K2,ℓ -minor free graphs
- On the maximum degree and order of Kt-minor-free graphs with positive Lin--Lu--Yau curvature
BibTeX
@misc{lin2026separators,
title = {{On separators in $K_t$-minor-free graphs}},
author = {Xinheng Lin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40270},
eprint = {2610.40270},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.40270},
}
RIS
TY - UNPB
TI - On separators in K_t-minor-free graphs
AU - Xinheng Lin
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.40270
UR - https://arxiv.org/abs/2610.40270
AB - This manuscript presents a proof of the Alon--Seymour--Thomas conjecture developed under the author's guidance using ChatGPT 6pro. The author has checked every formula and theorem by hand and used Codex to assist with writing. GPT 6.1 Sol (Max) was also used to check the proof repeatedly and to generate numerous examples for verification. More precisely, for every integer h≥3, every n-vertex K_h-minor-free graph has a vertex set of size at most minn,21h√n whose deletion leaves every component with at most 2n/3 vertices.
ER -