{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T18:09:55Z","timestamp":1758823795272,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Given a graph $G$ and positive integers $n$ and $q$, let ${\\bf G}(G;n,q)$ be the game played on the edges of the complete graph $K_n$ in which the two players, Maker and Breaker, alternately claim $1$ and $q$ edges, respectively. Maker's goal is to occupy all edges in some copy of $G$; Breaker tries to prevent it. In their seminal paper on positional games, Chv\u00e1tal and Erd\u0151s proved that in the game ${\\bf G}(K_3;n,q)$, Maker has a winning strategy if $q  &lt;  \\sqrt{2n+2}-5\/2$, and if $q \\geq 2\\sqrt{n}$, then Breaker has a winning strategy. In this note, we improve the latter of these bounds by describing a randomized strategy that allows Breaker to win the game ${\\bf G}(K_3;n,q)$ whenever $q \\geq (2-1\/24)\\sqrt{n}$. Moreover, we provide additional evidence supporting the belief that this bound can be further improved to $(\\sqrt{2}+o(1))\\sqrt{n}$.<\/jats:p>","DOI":"10.37236\/559","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T22:51:53Z","timestamp":1578696713000},"source":"Crossref","is-referenced-by-count":5,"title":["On the Chv\u00e1tal-Erd\u0151s Triangle Game"],"prefix":"10.37236","volume":"18","author":[{"given":"J\u00f3zsef","family":"Balogh","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wojciech","family":"Samotij","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2011,3,31]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p72\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p72\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T18:14:47Z","timestamp":1579284887000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v18i1p72"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,3,31]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2011,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/559","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2011,3,31]]},"article-number":"P72"}}