The second player colors a region, but again, it must be a region that does not share a boundary with a region that is already colored in the color that the second player is using. Notice, however, that two regions can be the same color if they meet only at a single point. A boundary has to be a line. The game ends when one of the players is unable to find a region to color. That player loses.
Coloring appears over and over again in mathematics.
Map coloring is a topic that has been studied for many years. Mathematicians have also thought about ways that knots can be colored. The game of Snort is a variation on the game of Col and also involves coloring maps.