{"paper":{"title":"A new Bound for the Maker-Breaker Triangle Game","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Anand Srivastav, Christian Glazik","submitted_at":"2018-12-04T12:44:09Z","abstract_excerpt":"The triangle game introduced by Chv\\'{a}tal and Erd\\H{o}s (1978) is one of the most famous combinatorial games. For $n,q\\in\\mathbb{N}$, the $(n,q)$-triangle game is played by two players, called Maker and Breaker, on the complete graph $K_n$. Alternately Maker claims one edge and thereafter Breaker claims $q$ edges of the graph. Maker wins the game if he can claim all three edges of a triangle, otherwise Breaker wins. Chv\\'{a}tal and Erd\\H{o}s (1978) proved that for $q<\\sqrt{2n+2}-5/2\\approx 1.414\\sqrt{n}$ Maker has a winning strategy, and for $q\\geq 2\\sqrt{n}$ Breaker has a winning strategy. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.01382","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":""},"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"}