I'm making a simple hex-based game, and I want the map to be divided evenly among the players. The map is created randomly, and I want the players to have about equal amount of cells, with relatively small areas. For example, if there's four players and 80 cells in the map, each of the players would have about 20 cells (it doesn't have to be spot-on accurate). Also, each player should have no more than four adjacent cells. That is to say, when the map is generated, the biggest "chunks" cannot be more than four cells each.

I know this is not always possible for two or three players (as this resembles the "coloring the map" problem), and I'm OK with doing other solutions for those (like creating maps that solve the problem instead). But, for four to eight players, how could I approach this problem?

As always, any and all help is appreciated. :)