{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:39:27Z","timestamp":1787319567904,"version":"build-2736575974"},"reference-count":38,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Discrete Math."],"published-print":{"date-parts":[[2023,6,30]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>We introduce a new type of positional games, played on a vertex set of a graph. Given a graph [Formula: see text], two players claim vertices of [Formula: see text], where the outcome of the game is determined by the subgraphs of [Formula: see text] induced by the vertices claimed by each player (or by one of them). We study classical positional games such as Maker-Breaker, Avoider-Enforcer, Waiter-Client, and Client-Waiter games, in both their biased and unbiased versions, where the board of the game is the vertex set of the binomial random graph [Formula: see text]. Under these settings, we consider those games where the target sets are the vertex sets of all graphs containing a copy of a fixed graph [Formula: see text], called [Formula: see text]-games. We focus on the cases in which [Formula: see text] is a clique, a cycle, or a forest, and for Waiter-Client and monotone Avoider-Enforcer games our results apply to any fixed graph [Formula: see text]. We show that, similarly to the edge version of [Formula: see text]-games, there is a strong connection between the threshold probability for these games and the one for the corresponding vertex Ramsey property (that is, the property that every [Formula: see text]-vertex-coloring of [Formula: see text] spans a monochromatic copy of [Formula: see text]). Another similarity to the edge version of these games we demonstrate is that the games in which [Formula: see text] is a triangle or a forest present a different behavior compared to the general case.<\/jats:p>","DOI":"10.1137\/20m1375991","type":"journal-article","created":{"date-parts":[[2023,6,9]],"date-time":"2023-06-09T04:44:18Z","timestamp":1686285858000},"page":"864-916","source":"Crossref","is-referenced-by-count":0,"title":["\\(\\boldsymbol{H}\\)-Games Played on Vertex Sets of Random Graphs"],"prefix":"10.1137","volume":"37","author":[{"given":"Gal","family":"Kronenberg","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, 6997801, Israel, and Mathematical Institute, University of Oxford, Oxford, UK."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4805-7503","authenticated-orcid":true,"given":"Adva","family":"Mond","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, 6997801, Israel, and Department of Pure Mathematics and Mathematical Statistics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB, UK."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alon","family":"Naor","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, 6997801, Israel."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2023,6,9]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511735202"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1007\/s004930200009"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.37236\/3095"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2012.12.037"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2019.01.003"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2015.12.008"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1007\/s004930070002"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20392"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511814068"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1007\/BF02579198"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-5060(08)70335-2"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548312000375"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.37236\/6039"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20528"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2013.09.008"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1090\/S0894-0347-99-00305-7"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781316339831"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20279"},{"key":"ref19","first-page":"145","volume":"17","author":"Grzesik A.","year":"2015","journal-title":"Discrete Math. 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