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Given a graph $$G=(V,E)$$ G = ( V , E ) , Alice and Bob, alternate their turns in choosing uncoloured edges to be coloured. Whenever an uncoloured edge is chosen, it is coloured by the least positive integer not used by any of its coloured neighbours. Alice’s goal is to minimize the total number of colours used in the game, and Bob’s goal is to maximize it. The game Grundy index of $$G$$...
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