Pure Simplicial and Clique Complexes with a Fixed Number of Facets
Combinatorics
2024-11-21 v1
Abstract
We study structural and enumerative aspects of pure simplicial complexes and clique complexes. We prove a necessary and sufficient condition for any simplicial complex to be a clique complex that depends only on the list of facets. We also prove a theorem that a class of ``triangle-intersection free" pure clique complexes are uniquely determined up to isomorphism merely from the facet-adjacency matrix. Lastly, we count the number of pure simplicial complexes with a fixed number of facets and find an upper bound to the number of pure clique complexes.
Keywords
Cite
@article{arxiv.2411.12945,
title = {Pure Simplicial and Clique Complexes with a Fixed Number of Facets},
author = {Kassahun H Betre and Yan X Zhang and Carter Edmond},
journal= {arXiv preprint arXiv:2411.12945},
year = {2024}
}