{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,15]],"date-time":"2026-10-15T13:30:28Z","timestamp":1792071028400,"version":"4.4.0"},"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>We consider the fair Hamiltonian cycle Maker-Breaker game, played on the edge set of the complete graph $K_n$ on $n$ vertices. It is known that Maker wins this game if $n$ is sufficiently large. We are interested in the minimum number of moves needed for Maker in order to win the Hamiltonian cycle game, and in the smallest $n$ for which Maker has a winning strategy for this game. We prove the following results: (1) If $n$ is sufficiently large, then Maker can win the Hamiltonian cycle game within $n+1$ moves. This bound is best possible and it settles a question of Hefetz, Krivelevich, Stojakovi\u0107 and Szab\u00f3; (2) If $n \\geq 29$, then Maker can win the Hamiltonian cycle game. This improves the previously best bound of $600$ due to Papaioannou.<\/jats:p>","DOI":"10.37236\/117","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:33:31Z","timestamp":1578717211000},"source":"Crossref","is-referenced-by-count":21,"title":["On Two Problems Regarding the Hamiltonian Cycle Game"],"prefix":"10.37236","volume":"16","author":[{"given":"Dan","family":"Hefetz","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sebastian","family":"Stich","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"23455","published-online":{"date-parts":[[2009,2,27]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r28\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r28\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T03:12:26Z","timestamp":1579317146000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v16i1r28"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,2,27]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2009,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/117","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,2,27]]},"article-number":"R28"}}