Map-coloring Games - Monochrome and Variants

Monochrome and Variants

These games, which appeared in (Silverman, 1971), all use the classical move constraint. In the impartial game Monochrome there is only one color available, so every move removes the colored region and its neighbors from play. In Bichrome both players have a choice of two colors, subject to the classical condition. Both players choose from the same two colors, so the game is impartial. Trichrome extends this to three colors to the players. The condition can be extended to any fixed number of colors, yielding further games. As Silverman mentions, although the Four color theorem shows that any planar map can be colored with four colors, it does not apply to maps in which some of the colors have been filled in, so adding more than four colors may have an effect on the games.