{"paper":{"title":"Chromatic roots at 2 and at the Beraha number $B_{10}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Daniel J. Harvey, Gordon F. Royle","submitted_at":"2018-07-23T01:45:46Z","abstract_excerpt":"By the construction of suitable graphs and the determination of their chromatic polynomials, we resolve two open questions concerning real chromatic roots. First we exhibit graphs for which the Beraha number $B_{10} = (5 + \\sqrt{5})/2$ is a chromatic root. As it was previously known that no other non-integer Beraha number is a chromatic root, this completes the determination of precisely which Beraha numbers can be chromatic roots. Next we construct an infinite family of $3$-connected graphs such that for any $k \\geqslant 1$, there is a member of the family with $q=2$ as a chromatic root of mu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.08397","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":""},"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"}