{"paper":{"title":"Network Representation and Modular Decomposition of Combinatorial Structures: A Galled-Tree Perspective","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Anna Lindeberg, Guillaume E. Scholz, Marc Hellmuth","submitted_at":"2024-06-26T19:28:05Z","abstract_excerpt":"In phylogenetics, reconstructing rooted trees from distances between taxa is a common task. B\\\"ocker and Dress generalized this concept by introducing symbolic dated maps $\\delta:X \\times X \\to \\Upsilon$, where distances are replaced by symbols, and showed that there is a one-to-one correspondence between symbolic ultrametrics and labeled rooted phylogenetic trees. Many combinatorial structures fall under the umbrella of symbolic dated maps, such as 2-dissimilarities, symmetric labeled 2-structures, or edge-colored complete graphs, and are here referred to as strudigrams. Strudigrams have a un"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.18713","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/2406.18713/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"}