English

The Linking-Unlinking Game

Geometric Topology 2019-10-30 v1 Combinatorics

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

Cite

@article{arxiv.1807.11026,
  title  = {The Linking-Unlinking Game},
  author = {Adam Giambrone and Jake Murphy},
  journal= {arXiv preprint arXiv:1807.11026},
  year   = {2019}
}

Comments

34 pages, 30 figures

R2 v1 2026-06-23T03:18:09.074Z