An Algorithmic Analysis of the Honey-Bee Game

The Honey-Bee game is a two-player board game that is played on a connected hexagonal colored grid, or in a generalized setting, on a connected graph with colored nodes. In a single move, a player calls a color and thereby conquers all nodes of that color that are adjacent to his own territory. Both players want to conquer the majority of the nodes. We show that winning the game is PSPACE-hard in general, NP-hard on series-parallel graphs, but easy on outerplanar graphs. The solitaire version, where the goal is to conquer the entire graph with a minimum number of moves, is NP-hard on trees and split graphs, but can be solved in polynomial time on co-comparability graphs.