The Kelmans-Seymour conjecture IV: a proof
Combinatorics
2016-12-22 v1
Abstract
A well known theorem of Kuratowski in 1932 states that a graph is planar if, and only if, it does not contain a subdivision of or . Wagner proved in 1937 that if a graph other than does not contain any subdivision of then it is planar or it admits a cut of size at most 2. Kelmans and, independently, Seymour conjectured in the 1970s that if a graph does not contain any subdivision of then it is planar or it admits a cut of size at most 4. In this paper, we give a proof of the Kelmans-Seymour conjecture. We also discuss several related results and problems.
Cite
@article{arxiv.1612.07189,
title = {The Kelmans-Seymour conjecture IV: a proof},
author = {Dawei He and Yan Wang and Xingxing Yu},
journal= {arXiv preprint arXiv:1612.07189},
year = {2016}
}