Resolution of Conjectures related to Lights Out! and Cartesian Products

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Bryan A Curtis
Jonathan Earl
David Livingston
Bryan L Shader


Lights Out! is a game played on a $5 \times 5$ 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.

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