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arXiv:1804.02385math.CO

The chromatic number of the plane is at least 5

Aubrey D. N. J. de Grey

Abstract

We present a family of finite unit-distance graphs in the plane that are not 4-colourable, thereby improving the lower bound of the Hadwiger-Nelson problem. The smallest such graph that we have so far discovered has 1581 vertices.

arXiv comments
Journal reference
DOI
Subjects
math.COCombinatorics

On Hacker News

Linked by 2 identifiable commenters in 2 comments across 2 threads, from Apr 2018 to Jun 2019. Found in 5 HN submissions from Apr 2018 to May 2018. Open submission discussions.

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Discussed in comments2 threads

  1. With greater longevity, the quest to avoid infirmities of aging is more urgent 1 comment

    • Could be but he also published a well-received paper on graph coloring, so at least he's not stupid. https://arxiv.org/abs/1804.02385

      ameliusView on HNParent context

  2. Decades-Old Graph Problem Yields to Amateur Mathematician 1 comment

    • The paper has beautiful illustrations. https://arxiv.org/pdf/1804.02385.pdf Animations showing how the larger graphs are built from smaller graphs would be amazing and illustrative for mortal non-mathematical-geniuses.

      gowldView on HNParent context

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