Abstract
A graph construction game is a Maker–Breaker game. Maker and Breaker take turns in choosing previously unoccupied edges of the complete graphKN. Maker's aim is to claim a copy of a given target graphGwhile Breaker's aim is to prevent Maker from doing so. In this paper we show that ifGis ad-degenerate graph onnvertices andN>d1122d+9n, then Maker can claim a copy ofGin at mostd1122d+7nrounds. We also discuss a lower bound on the number of rounds Maker needs to win, and the gap between these bounds.
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