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arXiv · 2411.08245

Vertex orders in higher dimensions

Bennet Goeckner·Marta Pavelka
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Abstract

Unit interval and interval complexes are higher-dimensional generalizations of unit interval and interval graphs, respectively. We show that strongly connected unit interval complexes are shellable with shellings induced by their unit interval orders. We also show that these complexes are vertex decomposable and hence shelling completable. On the other hand, we give simple examples of strongly connected interval complexes that are not shellable in dimensions two and higher.

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Bennet Goeckner, Marta Pavelka. 2024-11-12. Vertex orders in higher dimensions. https://arxiv.org/abs/2411.08245

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