The linking-unlinking game

Abstract

Combinatorial two-player games have recently been applied to knot theory. Examples of this include the knotting-unknotting game and the region unknotting game, both of which are played on knot shadows. These are turn-based games played by two players, where each player has a separate goal to achieve in order to win the game. In this paper, we introduce the linking-unlinking game which is played on two-component link shadows. We then present winning strategies for the linking-unlinking game played on all shadows of two-component rational tangle closures and played on a large family of general two-component link shadows.