Involve: A Journal of Mathematics

  • Involve
  • Volume 12, Number 7 (2019), 1109-1141.

The linking-unlinking game

Adam Giambrone and Jake Murphy

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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.

Article information

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

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45} 91A46: Combinatorial games

knot knot diagram link link diagram linking-unlinking game pseudodiagram rational link rational tangle splittable two-player game unsplittable winning strategy


Giambrone, Adam; Murphy, Jake. The linking-unlinking game. Involve 12 (2019), no. 7, 1109--1141. doi:10.2140/involve.2019.12.1109.

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