On Hajnal's triangle-free game

Abstract

We investigate the triangle-free game proposed by Andras Hajnal. Starting with the empty graph onn points, two players alternatingly pick edges. The loser is the player who is forced to select an edge which completes a triangle. We determine the winner in a version of the game with the additional rule that the chosen edges must always give a connected subgraph ofK n . Some other versions are also investigated.