{"paper":{"title":"From Modular Decomposition Trees to Rooted Median Graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Carmen Bruckmann, Marc Hellmuth, Peter F. Stadler","submitted_at":"2021-03-11T14:15:24Z","abstract_excerpt":"The modular decomposition of a symmetric map $\\delta\\colon X\\times X \\to \\Upsilon$ (or, equivalently, a set of symmetric binary relations, a 2-structure, or an edge-colored undirected graph) is a natural construction to capture key features of $\\delta$ in labeled trees. A map $\\delta$ is explained by a vertex-labeled rooted tree $(T,t)$ if the label $\\delta(x,y)$ coincides with the label of the last common ancestor of $x$ and $y$ in $T$, i.e., if $\\delta(x,y)=t(\\mathrm{lca}(x,y))$. Only maps whose modular decomposition does not contain prime nodes, i.e., the symbolic ultrametrics, can be exapl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2103.06683","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2103.06683/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"}