{"paper":{"title":"Constant Threshold Intersection Graphs of Orthodox Paths in Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Claudson Ferreira Bornstein, Dieter Rautenbach, Jayme Luiz Szwarcfiter, Jos\\'e Wilson Coura Pinto","submitted_at":"2017-03-24T15:35:22Z","abstract_excerpt":"A graph $G$ belongs to the class ${\\rm ORTH}[h,s,t]$ for integers $h$, $s$, and $t$ if there is a pair $(T,{\\cal S})$, where $T$ is a tree of maximum degree at most $h$, and ${\\cal S}$ is a collection $(S_u)_{u\\in V(G)}$ of subtrees $S_u$ of maximum degree at most $s$ of $T$, one for each vertex $u$ of $G$, such that, for every vertex $u$ of $G$, all leaves of $S_u$ are also leaves of $T$, and, for every two distinct vertices $u$ and $v$ of $G$, the following three properties are equivalent:\n  (i) $u$ and $v$ are adjacent.\n  (ii) $S_u$ and $S_v$ have at least $t$ vertices in common.\n  (iii) $S"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.08465","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"}