Games on triangulations

We analyze several perfect-information combinatorial games played on planar triangulations. We introduce three broad categories of such games—constructing, transforming, and marking triangulations—and several specific games within each category. In various situations of each game, we develop polynomial-time algorithms to determine who wins a given game position under optimal play, and to find a winning strategy. Along the way, we show connections to existing combinatorial games such as Kayles and Nimstring (a variation on Dots-and-Boxes).