{"paper":{"title":"On problems in extremal multigraph theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Adva Mond, Rik Sarkar, Victor Falgas-Ravry, Victor Souza","submitted_at":"2025-05-20T12:32:08Z","abstract_excerpt":"A multigraph G is said to be an (s,q)-graph if every s-set of vertices in G supports at most q edges (counting multiplicities). In this paper we consider the maximal sum and product of edge multiplicities in an (s,q)-graph on n vertices. These are multigraph analogues of a problem of Erd\\H{o}s raised by F\\\"uredi and K\\\"undgen and Mubayi and Terry respectively, with applications to counting problems and extremal hypergraph theory.\n  We make major progress, settling conjectures of Day, Falgas-Ravry and Treglown and of Falgas-Ravry, establishing intricate behaviour for both the sum and the produc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.14281","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/2505.14281/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"}