{"paper":{"title":"Mutual-visibility of the disjointness graph of segments in ${\\mathbb R}^2$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Christophe Ndjatchi, J. Lea\\~nos, L. M. R\\'ios-Castro, M. Lomel\\'i-Haro","submitted_at":"2025-05-31T19:46:38Z","abstract_excerpt":"Let $G=(V(G),E(G))$ be a simple graph, and let $U\\subseteq V(G)$. Two distinct vertices $x,y\\in U$ are $U$-mutually visible if $G$ contains a shortest $x$-$y$ path that is internally disjoint from $U$. $U$ is called a mutual-visibility set of $G$ if any two vertices of $U$ are $U$-mutually visible. The mutual-visibility number $\\mu(G)$ of $G$ is the size of a largest mutual-visibility set of $G$. Let $P$ be a set of $n\\geq 3$ points in ${\\mathbb R}^2$ in general position. The disjointness graph of segments $D(P)$ of $P$ is the graph whose vertices are all the closed straight line segments with"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.00689","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.00689/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}