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  "path": "/abs/2603.01244v1",
  "publishedAt": "2026-03-03T01:00:00.000Z",
  "site": "https://arxiv.org",
  "tags": [
    "Linus Klocker",
    "Simon D. Fink"
  ],
  "textContent": "**Authors:** Linus Klocker, Simon D. Fink\n\nMany 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.",
  "title": "Hexasort -- The Complexity of Stacking Colors on Graphs"
}