{"paper":{"title":"Coloring non-crossing strings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"math.CO","authors_text":"Arnaud Labourel, Daniel Gon\\c{c}alves, Louis Esperet","submitted_at":"2015-11-12T09:25:00Z","abstract_excerpt":"For a family of geometric objects in the plane $\\mathcal{F}=\\{S_1,\\ldots,S_n\\}$, define $\\chi(\\mathcal{F})$ as the least integer $\\ell$ such that the elements of $\\mathcal{F}$ can be colored with $\\ell$ colors, in such a way that any two intersecting objects have distinct colors. When $\\mathcal{F}$ is a set of pseudo-disks that may only intersect on their boundaries, and such that any point of the plane is contained in at most $k$ pseudo-disks, it can be proven that $\\chi(\\mathcal{F})\\le 3k/2 + o(k)$ since the problem is equivalent to cyclic coloring of plane graphs. In this paper, we study th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.03827","kind":"arxiv","version":2},"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"}