{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:33:31Z","timestamp":1787322811791,"version":"build-2736575974"},"reference-count":17,"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":[[2013,1]]},"abstract":"<jats:p>Given a graph $G$ and an integer $k$, two players take turns coloring the vertices of $G$ one by one using $k$ colors so that neighboring vertices get different colors. The first player wins iff at the end of the game all the vertices of $G$ are colored. The game chromatic number $\\chi_g(G)$ is the minimum $k$ for which the first player has a winning strategy. The paper [T. Bohman, A. M. Frieze, and B. Sudakov, Random Structures Algorithms, 32 (2008), pp. 223--235] began the analysis of the asymptotic behavior of this parameter for a random graph $G_{n,p}$. This paper provides some further analysis for graphs with constant average degree, i.e., $np=O(1)$, and for random regular graphs. We show that with high probability (w.h.p.) $c_1\\chi(G_{n,p})\\leq \\chi_g(G_{n,p})\\leq c_2\\chi(G_{n,p})$ for some absolute constants $1&lt;c_1&lt; c_2$. We also prove that if $G_{n,3}$ denotes a random $n$-vertex cubic graph, then w.h.p. $\\chi_g(G_{n,3})=4$.<\/jats:p>","DOI":"10.1137\/120861953","type":"journal-article","created":{"date-parts":[[2013,4,18]],"date-time":"2013-04-18T11:09:58Z","timestamp":1366283398000},"page":"768-790","source":"Crossref","is-referenced-by-count":3,"title":["On the Game Chromatic Number of Sparse Random Graphs"],"prefix":"10.1137","volume":"27","author":[{"given":"Alan","family":"Frieze","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Simcha","family":"Haber","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mikhail","family":"Lavrov","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2013,4,18]]},"reference":[{"key":"atypb1","first-page":"219","author":"Achlioptas D.","year":"2004","journal-title":"New York"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.4007\/annals.2005.162.1335"},{"key":"atypb3","doi-asserted-by":"crossref","unstructured":"N. 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Ruci\u0144ski,<i>Random Graphs<\/i> John Wiley, New York, 2000.","DOI":"10.1002\/9781118032718"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1016\/j.aim.2009.08.006"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1016\/j.aim.2003.10.007"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1007\/BF01375472"},{"key":"atypb17","first-page":"239","author":"Wormald N.","year":"1999","journal-title":"UK"}],"container-title":["SIAM Journal on Discrete Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/120861953","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:26:47Z","timestamp":1787318807000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/120861953"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,1]]},"references-count":17,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2013,1]]}},"alternative-id":["10.1137\/120861953"],"URL":"https:\/\/doi.org\/10.1137\/120861953","relation":{},"ISSN":["0895-4801","1095-7146"],"issn-type":[{"value":"0895-4801","type":"print"},{"value":"1095-7146","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,1]]}}}