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In each round Painter colours a vertex of her choice by one of the $k$ colours and Builder claims an edge between two previously unconnected vertices. Both players should maintain that during the game the graph admits a proper $k$-colouring. The game ends if either all $n$ vertices have been coloured, or Painter has no legal move. 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The game is played between Painter and Builder, alternately taking turns, with Painter moving first. The game starts with the empty graph on $n$ vertices. In each round Painter colours a vertex of her choice by one of the $k$ colours and Builder claims an edge between two previously unconnected vertices. Both players should maintain that during the game the graph admits a proper $k$-colouring. The game ends if either all $n$ vertices have been coloured, or Painter has no legal move. 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