{"paper":{"title":"Solving Maker-Breaker Games on 5-uniform hypergraphs is PSPACE-complete","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Finn Orson Koepke","submitted_at":"2025-02-27T16:57:05Z","abstract_excerpt":"Let $(X, \\mathcal{F})$ be a hypergraph. The Maker-Breaker game on $(X, \\mathcal{F})$ is a combinatorial game between two players, Maker and Breaker. Beginning with Maker, the players take turns claiming vertices from $X$ that have not yet been claimed. Maker wins if she manages to claim all vertices of some hyperedge $F \\in \\mathcal{F}$. Breaker wins if he claims at least one vertex in every hyperedge.\n  M. L. Rahman and Thomas Watson proved in 2021 that, even when only Maker-Breaker games on 6-uniform hypergraphs are considered, the decision problem of determining which player has a winning s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.20271","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/2502.20271/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"}