Vexing vexillological logic

Kyle Burke () and Craig Tennenhouse ()
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Kyle Burke: Florida Southern College
Craig Tennenhouse: University of New England

International Journal of Game Theory, 2024, vol. 53, issue 4, No 6, 1187-1210

Abstract: Abstract We define a new impartial combinatorial game, FLAG COLORING, based on flood filling, and find some values and outcome classes for some game positions. We then generalize FLAG COLORING to a graph game, re-imagining the game on two colors as an edge-reduction game on graphs, and find values for many positions represented as graph families on two colors. We demonstrate that the generalized game is PSPACE-complete for two or more colors via a reduction from AVOID TRUE. Finally, remaining open problems are discussed.

Keywords: Impartial; Combinatorial game; Flood fill; Complexity; PSPACE (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00182-024-00899-y

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