Involve: A Journal of Mathematics
- Volume 12, Number 7 (2019), 1109-1141.
The linking-unlinking game
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.
Involve, Volume 12, Number 7 (2019), 1109-1141.
Received: 30 July 2018
Revised: 17 May 2019
Accepted: 11 June 2019
First available in Project Euclid: 26 October 2019
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Giambrone, Adam; Murphy, Jake. The linking-unlinking game. Involve 12 (2019), no. 7, 1109--1141. doi:10.2140/involve.2019.12.1109. https://projecteuclid.org/euclid.involve/1572055223