Vexing vexillological logic

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.