{"paper":{"title":"Extremal Restraints for Graph Colourings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Aysel Erey, Jason I. Brown, Jian Li","submitted_at":"2016-11-27T22:07:34Z","abstract_excerpt":"A {\\em restraint} on a (finite undirected) graph $G = (V,E)$ is a function $r$ on $V$ such that $r(v)$ is a finite subset of ${\\mathbb N}$; a proper vertex colouring $c$ of $G$ is {\\em permitted} by $r$ if $c(v) \\not\\in r(v)$ for all vertices $v$ of $G$ (we think of $r(v)$ as the set of colours {\\em forbidden} at $v$). Given a large number of colors, for restraints $r$ with exactly one colour forbidden at each vertex the smallest number of colorings is permitted when $r$ is a constant function, but the problem of what restraints permit the largest number of colourings is more difficult. We det"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.08920","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"}