{"paper":{"title":"The chromatic number of finite projective spaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ananthakrishnan Ravi, Anurag Bishnoi, Wouter Cames van Batenburg","submitted_at":"2025-12-01T15:05:26Z","abstract_excerpt":"The chromatic number of the finite projective space $\\mathrm{PG}(n-1,q)$, denoted $\\chi_q(n)$, is the minimum number of colors needed to color its points so that no line is monochromatic. We prove subadditivity of $\\chi_q(n)$ with respect to $n$, and then establish the following stronger recursive bound: \\[ \\chi_q(n)\\le \\chi_q(d)+\\chi_q(n+1-d)-1 \\] for all $1 \\leq d < n$. We use it to prove new upper bounds on $\\chi_q(n)$. For $q = 2$, using this recursion we prove that \\[ \\chi_2(n) \\le \\lfloor 2n/3 \\rfloor + 1 \\] for all $n \\ge 2$, and we show that this bound is tight for all $n \\le 7$. In pa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.01760","kind":"arxiv","version":3},"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/2512.01760/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"}