The Game of Cycles
Combinatorics
2020-04-03 v1 General Topology
Abstract
The Game of Cycles, introduced by Su (2020), is played on a simple connected planar graph together with its bounded cells, and players take turns marking edges with arrows according to a sink-source rule that gives the game a topological flavor. The object of the game is to produce a cycle cell---a cell surrounded by arrows all cycling in one direction---or to make the last possible move. We analyze the two-player game for various classes of graphs and determine who has a winning strategy. We also establish a topological property of the game: that a board with every edge marked must have a cycle cell.
Keywords
Cite
@article{arxiv.2004.00776,
title = {The Game of Cycles},
author = {Ryan Alvarado and Maia Averett and Benjamin Gaines and Christopher Jackson and Mary Leah Karker and Malgorzata Aneta Marciniak and Francis Su and Shanise Walker},
journal= {arXiv preprint arXiv:2004.00776},
year = {2020}
}
Comments
20 pages, 22 figures