{"paper":{"title":"Unified framework for asymptotically uniform iterative construction of generalised random graphs with local constraints","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Ivan Kryven, Mike de Vries, Rik Versendaal","submitted_at":"2026-08-07T13:57:54Z","abstract_excerpt":"We develop a unified framework for constructing combinatorial structures under local constraints. Our approach extends the configuration model for random graphs with a prescribed degree sequence, and covers many special cases, including bipartite graphs, directed graphs, oriented graphs, edge-colored (bipartite) graphs, and (directed) hypergraphs.\n  By reformulating half-edge matching as an independent set problem in an auxiliary graph, we identify 2-uniformity, a property characterising when greedy sampling preserves asymptotic uniformity. We classify all 2-uniform graphs and show that only t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.07239","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/2608.07239/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"}