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Given $n$ points $x_1, \\ldots,x_n$ in the plane, and a threshold $r>0$, the corresponding geometric graph has vertex set $\\{v_1,\\ldots,v_n\\}$, and distinct $v_i$ and $v_j$ are adjacent when the Euclidean distance between $x_i$ and $x_j$ is at most $r$. We investigate the clique chromatic number of such graphs.\n  We first show that the clique chromatic number is at most 9 for any ge"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1701.02693","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-01-10T17:15:26Z","cross_cats_sorted":[],"title_canon_sha256":"085bf491142e992f093a3676b8a852d17730b91e198f985bb1e9caf8fad24e18","abstract_canon_sha256":"be5110bf831f2a473a8298572d66dc11a64fafbbf5fb2506df0b04d12238e93c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:26.641403Z","signature_b64":"diMRl/OtUIVJ8SvovtGR3QAY4NXYG+DbSKeDRYX5Ja89XnLdnJFIwkKAMg4fgltb+Qj/AbXj0maqnPmK8rLuDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7a2ac4ecaf6b440e3b07e3a513dd05b723e40b797db3edb4d5c7dba4a4f1464a","last_reissued_at":"2026-05-17T23:59:26.640791Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:26.640791Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Clique colourings of geometric graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Colin McDiarmid, Dieter Mitsche, Pawel Pralat","submitted_at":"2017-01-10T17:15:26Z","abstract_excerpt":"A clique colouring of a graph is a colouring of the vertices such that no maximal clique is monochromatic (ignoring isolated vertices). 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