{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:15Z","timestamp":1753893795567,"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>In this note we investigate a special form of degree games defined by D. Hefetz, M. Krivelevich, M. Stojakovi\u0107 and T. Szab\u00f3. Usually the board of a graph game is the edge set of $K_n$, the complete graph on $n$ vertices. Maker and Breaker alternately claim an edge, and Maker wins if his edges form a subgraph with prescribed properties; here a certain minimum degree. In the special form the board is no longer the whole edge set of $K_n$, Maker first selects as few edges of $K_n$ as possible in order to win, and our goal is to compute the necessary size of that board. Solving a question of Hefetz et al., we show, using the discharging method, that the sharp bound is around $10n\/7$ for the positive minimum degree game. <\/jats:p>","DOI":"10.37236\/1174","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T22:32:55Z","timestamp":1578695575000},"source":"Crossref","is-referenced-by-count":1,"title":["The Positive Minimum Degree Game on Sparse Graphs"],"prefix":"10.37236","volume":"19","author":[{"given":"J\u00f3zsef","family":"Balogh","sequence":"first","affiliation":[]},{"given":"Andr\u00e1s","family":"Pluh\u00e1r","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2012,1,21]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v19i1p22\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v19i1p22\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T17:42:52Z","timestamp":1579282972000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v19i1p22"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,1,21]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2012,2,15]]}},"URL":"https:\/\/doi.org\/10.37236\/1174","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2012,1,21]]},"article-number":"P22"}}