{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:15Z","timestamp":1753893855921,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>We study the two-player game where Maker and Breaker alternately color the edges of a given graph $G$ with $k$ colors such that adjacent edges never get the same color. Maker's goal is to play such that at the end of the game, all edges are colored. Vice-versa, Breaker wins as soon as there is an uncolored edge where every color is blocked. The game chromatic index $\\chi'_g(G)$ denotes the smallest $k$ for which Maker has a winning strategy.The trivial bounds $\\Delta(G) \\le \\chi_g'(G) \\le 2\\Delta(G)-1$ hold for every graph $G$, where $\\Delta(G)$ is the maximum degree of $G$. Beveridge, Bohman, Frieze, and Pikhurko\u00a0conjectured that there exists a constant $c&gt;0$ such that for any graph $G$ it holds $\\chi'_g(G) \\le (2-c)\\Delta(G)$ [Theoretical Computer Science 2008], and verified the statement for all $\\delta&gt;0$ and all graphs with $\\Delta(G) \\ge (\\frac12+\\delta)|V(G)|$. In this paper, we show that $\\chi'_g(G) \\le (2-c)\\Delta(G)$ is true for all graphs $G$ with $\\Delta(G) \\ge C \\log |V(G)|$. In addition, we consider a biased version of the game where Breaker is allowed to color $b$ edges per turn and give bounds on the number of colors needed for Maker to win this biased game.<\/jats:p>","DOI":"10.37236\/7451","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T15:24:37Z","timestamp":1578669877000},"source":"Crossref","is-referenced-by-count":2,"title":["A New Upper Bound on the Game Chromatic Index of Graphs"],"prefix":"10.37236","volume":"25","author":[{"given":"Ralph","family":"Keusch","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2018,5,25]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i2p33\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i2p33\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:33:26Z","timestamp":1579235606000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v25i2p33"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,5,25]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2018,4,13]]}},"URL":"https:\/\/doi.org\/10.37236\/7451","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2018,5,25]]},"article-number":"P2.33"}}