Year: 2018
Type: preprint
Abstract: We present a new method for reducing the size of graphs with a given property. Our method, which is based on clausal proof minimization, allowed us to compute several 553-vertex unit-distance graphs with chromatic number 5, while the smallest published unit-distance graph with chromatic number 5 has 1581 vertices. The latter graph was constructed by Aubrey de Grey to show that the chromatic number of the plane is at least 5. The lack of a 4-coloring of our graphs is due to a clear pattern enforced on some vertices. Also, our graphs can be mechanically validated in a second, which suggests that the pattern is based on a reasonably short argument.
Source: arXiv (Cornell University)
Author: Heule, Marijn J. H.
Institution: The University of Texas at Austin
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: University of Texas at Austin
OpenAlex ID: W2806868982