{"paper":{"title":"Minimal and minimum unit circular-arc models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Francisco J. Soulignac, Pablo Terlisky","submitted_at":"2016-09-05T19:44:02Z","abstract_excerpt":"A proper circular-arc (PCA) model is a pair ${\\cal M} = (C, \\cal A)$ where $C$ is a circle and $\\cal A$ is a family of inclusion-free arcs on $C$ in which no two arcs of $\\cal A$ cover $C$. A PCA model $\\cal U = (C,\\cal A)$ is a $(c, \\ell)$-CA model when $C$ has circumference $c$, all the arcs in $\\cal A$ have length $\\ell$, and all the extremes of the arcs in $\\cal A$ are at a distance at least $1$. If $c \\leq c'$ and $\\ell \\leq \\ell'$ for every $(c', \\ell')$-CA model equivalent (resp. isomorphic) to $\\cal U$, then $\\cal U$ is minimal (resp. minimum). In this article we prove that every PCA m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.01266","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":""},"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"}