{"paper":{"title":"A Moser-spindle-free 5-chromatic unit distance graph on 2131 vertices in the plane","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jan Kristian Haugland","submitted_at":"2026-08-05T07:20:58Z","abstract_excerpt":"With regard to the Hadwiger-Nelson problem, several 5-chromatic unit distance graphs in the Euclidean plane have been discovered in recent years. While most constructions rely heavily on the Moser spindle, Voronov \\textit{et al.} found examples on 64513 vertices that completely avoid it. In this note, we improve upon this result by presenting a 5-chromatic unit distance graph on 2131 vertices that similarly does not contain the Moser spindle. It is constructed utilizing the arcs of a 7-fold symmetric unit distance graph on 21 vertices."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.04542","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.04542/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}