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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.\n  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 $G$. 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