Hexasort -- The Complexity of Stacking Colors on Graphs

Linus Klocker; Simon D. Fink

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arXiv · 2603.01244

Hexasort -- The Complexity of Stacking Colors on Graphs

Linus Klocker·Simon D. Fink

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Abstract

Many popular puzzle and matching games have been analyzed through the lens of computational complexity. Prominent examples include Sudoku, Candy Crush, and Flood-It. A common theme among these widely played games is that their generalized decision versions are NP-hard, which is often thought of as a source of their inherent difficulty and addictive appeal to human players. In this paper, we study a popular single-player stacking game commonly known as Hexasort. The game can be modelled as placing colored stacks onto the vertices of a graph, where adjacent stacks of the same color merge and vanish according to deterministic rules. We prove that Hexasort is NP-hard, even when restricted to single-color stacks and progressively more constrained classes of graphs, culminating in strong NP-hardness on trees of either bounded height or degree. Towards fixed-parameter tractable algorithms, we identify settings in which the problem becomes polynomial-time solvable and present dynamic programming algorithms.

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Linus Klocker, Simon D. Fink. 2026-03-01. Hexasort -- The Complexity of Stacking Colors on Graphs. https://arxiv.org/abs/2603.01244

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