Resolution of Conjectures Related to Lights Out! and Cartesian Products

2018/02/14 by Curtis, Bryan, Earl, Jonathan, Livingston, David +1
#Combinatorics (math.CO) #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1802.05359

Abstract

Lights Out! is a game played on a 5 × 5 grid of lights, or more generally on a graph. Pressing lights on the grid allows the player to turn off neighboring lights. The goal of the game is to start with a given initial configuration of lit lights and reach a state where all lights are out. Two conjectures posed in a recently published paper about Lights Out! on Cartesian products of graphs are resolved.

Related

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• An Inductive Proof that Lights Out Configurations are Invertible, and a Parity-Invariance Result
• Lights Out On Nearly Complete Graphs
• Most Clicks Problem in Lights Out