An Algorithmic Analysis of the Honey-Bee Game

TL;DR

This paper analyzes the computational complexity of the Honey-Bee game, revealing its hardness in general and specific graph classes, and providing polynomial solutions for certain cases.

Contribution

It establishes complexity bounds for the Honey-Bee game across various graph classes and identifies cases where the game is solvable efficiently.

Findings

Winning the game is PSPACE-hard in general.

NP-hard on series-parallel graphs.

Polynomial-time solution on co-comparability graphs.

Abstract

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 the nodes of that color that are adjacent to his own current 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. In the solitaire version, the goal of the single player is to conquer the entire graph with the minimum number of moves. The solitaire version is NP-hard on trees and split graphs, but can be solved in polynomial time on co-comparability graphs.