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The poset of maximal tubings of the cycle graph is a lattice
Ben Adenbaum, Emily Barnard, Max Hlavacek, Bryson Kagy, Nathan R. T. Lesnevich, George D. Nasr, Katie Waddle
https://arxiv.org/abs/2510.09429

The poset of maximal tubings of the cycle graph is a lattice
The poset of maximal tubings of a graph generalizes several well-known and remarkable partial orders. Notable examples include the weak Bruhat order and the Tamari lattice, posets of maximal tubings for the complete graph and the path graph, respectively. It is an open problem to characterize graphs for which the poset of maximal tubings is a lattice. In this paper, we prove that the poset of maximal tubings for the cycle graph is a lattice, and moreover that it is semidistributive and congruen…