The linking-unlinking game

Giambrone, Adam; Murphy, Jake

doi:10.2140/involve.2019.12.1109

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The linking-unlinking game

Adam Giambrone and Jake Murphy

Vol. 12 (2019), No. 7, 1109–1141

DOI: 10.2140/involve.2019.12.1109

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.

Keywords

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

Mathematical Subject Classification 2010

Primary: 57M25, 91A46

Milestones

Received: 30 July 2018

Revised: 17 May 2019

Accepted: 11 June 2019

Published: 12 October 2019

Communicated by Kenneth S. Berenhaut

Authors

Adam Giambrone
Elmira College Elmira, NY United States

Jake Murphy
Louisiana State University Baton Rouge, LA United States

Vol. 12, No. 7, 2019