Atropos-k is PSPACE-complete
<|reference_start|>Atropos-k is PSPACE-complete: Burke and Teng introduced a two-player combinatorial game Atropos based on Sperner's lemma, and showed that deciding whether one has a winning strategy for Atropos is PSPACE-complete. In the original Atropos game, the players must color a node adjacent to the last colored node. Burke and Teng also mentioned a variant Atropos-k in which each move is at most of distance k of the previous move, and asked a question on determining the computational complexity of this variant. In this paper, we answer this question by showing that for any fixed integer k (k>=2), Atropos-k is PSPACE-complete by reduction from True Quantified Boolean Formula (TQBF).<|reference_end|>
@article{yang2024atropos-k,
    title={Atropos-k is PSPACE-complete},
    author={Chao Yang, Zhujun Zhang},
    journal={arXiv preprint arXiv:2403.01662},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.01662},
    primaryClass={cs.CC cs.DM math.CO}
}