English

Vertex orders in higher dimensions

Combinatorics 2024-11-14 v1

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.

Keywords

Cite

@article{arxiv.2411.08245,
  title  = {Vertex orders in higher dimensions},
  author = {Bennet Goeckner and Marta Pavelka},
  journal= {arXiv preprint arXiv:2411.08245},
  year   = {2024}
}
R2 v1 2026-06-28T19:57:48.515Z