How Long Can a Graph be Kept Planar?

The graph (non-)planarity game is played on the complete graph Kn between an Enforcer and an Avoider, each of whom take one edge per round. The game ends when the edges chosen by Avoider form a non-planar subgraph. We show that Avoider can play for 3n− 26 turns, improving the previous bound of 3n− 28 √ n. 

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