{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:31Z","timestamp":1753893811845,"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>We investigate a game played on a hypergraph $H=(V,E)$ by two players, Balancer and Unbalancer. They select one element of the vertex set $V$ alternately until all vertices are selected. Balancer wins if at the end of the game all edges $e\\in E$ are roughly equally distributed between the two players. We give a polynomial time algorithm for Balancer to win provided the allowed deviation is large enough.  In particular, it follows from our result that if $H$ is $n$-uniform and has $m$ edges, then Balancer can achieve having between $n\/2-\\sqrt{\\ln(2m)n\/2}$ and $n\/2+\\sqrt{\\ln(2m)n\/2}$ of his vertices on every edge $e$ of $H$.  We also discuss applications in positional game theory.<\/jats:p>","DOI":"10.37236\/1948","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T05:09:23Z","timestamp":1578719363000},"source":"Crossref","is-referenced-by-count":4,"title":["Discrepancy Games"],"prefix":"10.37236","volume":"12","author":[{"given":"Noga","family":"Alon","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michael","family":"Krivelevich","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Joel","family":"Spencer","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tibor","family":"Szab\u00f3","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2005,9,29]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v12i1r51\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v12i1r51\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:40:42Z","timestamp":1579322442000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v12i1r51"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,9,29]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2005,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/1948","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2005,9,29]]},"article-number":"R51"}}