Abstract
The paper deals with σ-games on grid graphs (in dimension 2 and more) and conditions under which any completely symmetric configuration of lit vertices can be reached – in particular the completely lit configuration – when starting with the all-unlit configuration. The answer is complete in dimension 2. In dimension ≥3, the answer is complete for the σ +-game, and for the σ −-game if at least one of the sizes is even. The case σ −, dimension ≥3 and all sizes odd remains open.
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Florence, M., Meunier, F. Completely symmetric configurations for σ-games on grid graphs. J Algebr Comb 31, 533–545 (2010). https://doi.org/10.1007/s10801-009-0199-7
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DOI: https://doi.org/10.1007/s10801-009-0199-7