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arXiv · 1612.07189

The Kelmans-Seymour conjecture IV: a proof

Dawei He·Yan Wang·Xingxing Yu
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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 $K_5$ or $K_{3,3}$. Wagner proved in 1937 that if a graph other than $K_5$ does not contain any subdivision of $K_{3,3}$ 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 $K_5$ 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.

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Dawei He, Yan Wang, Xingxing Yu. 2016-12-21. The Kelmans-Seymour conjecture IV: a proof. https://arxiv.org/abs/1612.07189

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