The chromatic number of the plane is at least 5
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.
- Publication:
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arXiv e-prints
- Pub Date:
- April 2018
- DOI:
- arXiv:
- arXiv:1804.02385
- Bibcode:
- 2018arXiv180402385D
- Keywords:
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- Mathematics - Combinatorics