Strategy Stealing in Triangle Avoidance Games

Abstract

In the game of $n-Sim$, two players take it in turn to claim unclaimed edges from a complete graph on $n$ vertices, with the first person to create a triangle in his own edges being the loser. We present some strategy-stealing arguments that show that certain positions are wins for the second player. These are among the only strategy-stealing arguments that are known for mis\`ere games.