{"paper":{"title":"Encoding and Enumerating Acyclic Orientations of Graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Francisco Reyes, Jessica Khera, Walter Carballosa","submitted_at":"2023-03-16T01:24:27Z","abstract_excerpt":"In this work we study the acyclic orientations of graphs. We obtain an encoding of the acyclic orientations of the complete $p$-partite graph with size of its parts $n_1,n_2,\\ldots,n_p$ via a vector with $p$ symbols and length $n=n_1+n_2+\\ldots+n_p$ when the parts are fixed but not the vertices in each part. We also give a recursive way to construct all acyclic orientations of a complete multipartite graph, this construction can be done by computer easily in order $\\mathcal{O}(n)$. Furthermore, we obtain a closed formula for non-isomorphic acyclic orientations of both the complete multipartite"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.09021","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/2303.09021/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"}