A 2131-vertex unit-distance graph with chromatic number 5 and no Moser spindle is constructed from the arcs of a 7-fold symmetric 21-vertex graph.
Graph minimization, focusing on the example of 5-chromatic unit-distance graphs in the plane
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abstract
We introduce a new graph minimization method, in which it is required to preserve some graph property and there is an effective procedure for checking this property. We applied this method to minimize 5-chromatic unit-distance graphs and obtained a graph with 509 vertices and 2442 edges.
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A Moser-spindle-free 5-chromatic unit distance graph on 2131 vertices in the plane
A 2131-vertex unit-distance graph with chromatic number 5 and no Moser spindle is constructed from the arcs of a 7-fold symmetric 21-vertex graph.