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Graph minimization, focusing on the example of 5-chromatic unit-distance graphs in the plane

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arxiv 2010.12665 v2 pith:UTBNG36I submitted 2020-10-23 math.CO math.MG

Jaan Parts This is my paper · ORCID
classification math.COmath.MG
keywords graphchromaticgraphsmethodminimizationpropertyunit-distanceapplied
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. A Moser-spindle-free 5-chromatic unit distance graph on 2131 vertices in the plane

    math.CO 2026-08 conditional novelty 6.0 of 10

    A new 2131-vertex unit distance graph requiring 5 colors and containing no Moser spindle is constructed from the arcs of a 7-fold symmetric 21-vertex graph.

  2. Neural Discovery in Mathematics: Do Machines Dream of Colored Planes?

    cs.LG 2025-01 conditional novelty 6.0 of 10

    A neural network relaxation of geometric coloring constraints produced new plane colorings, including an almost 5-coloring covering all but 3.74% of the plane, improving known bounds for Hadwiger-Nelson variants.

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