Some remarks on the Game of Cycles

TL;DR

This paper discusses the Game of Cycles, an impartial game on planar graphs, addressing existing questions and proposing new ones to deepen understanding of the game's properties.

Contribution

It provides insights into the Game of Cycles, clarifies some open questions, and introduces new research directions for the game on planar graphs.

Findings

Clarified certain properties of the Game of Cycles

Raised new questions for future research

Provided insights into game strategies on planar graphs

Abstract

The Game of Cycles is an impartial game on a planar graph that was introduced by Francis Su. In this short note we address some questions that have been raised on the game, and raise some further questions.