{"paper":{"title":"Max Point-Tolerance Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Bjarni V. Halld\\'orsson, Daniele Catanzaro, Juraj Stacho, Magn\\'us M. Halld\\'orsson, Stefan Felsner, Steven Chaplick, Thomas Hixon","submitted_at":"2015-08-16T11:12:23Z","abstract_excerpt":"A graph $G$ is a \\emph{max point-tolerance (MPT)} graph if each vertex $v$ of $G$ can be mapped to a \\emph{pointed-interval} $(I_v, p_v)$ where $I_v$ is an interval of $\\mathbb{R}$ and $p_v \\in I_v$ such that $uv$ is an edge of $G$ iff $I_u \\cap I_v \\supseteq \\{p_u, p_v\\}$. MPT graphs model relationships among DNA fragments in genome-wide association studies as well as basic transmission problems in telecommunications. We formally introduce this graph class, characterize it, study combinatorial optimization problems on it, and relate it to several well known graph classes. We characterize MPT "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.03810","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"}