Line graphs of simplicial complexes
Commutative Algebra
2025-09-16 v4 Combinatorics
Abstract
We consider the line graph of a pure simplicial complex. We prove that, as in the case of line graphs of simple graphs, one can compute the second graded Betti number of the facet ideal of a pure simplicial complex in terms of the combinatorial structure of its line graph. We characterize those pure simplicial complexes whose line graph is a complete (bipartite) graph. We give conditions that line graphs of simplicial complexes should fulfill.
Cite
@article{arxiv.2206.13463,
title = {Line graphs of simplicial complexes},
author = {Anda Olteanu},
journal= {arXiv preprint arXiv:2206.13463},
year = {2025}
}
Comments
We split the previous version into two papers. This version corrects Theorem 4.5 and Proposition 5.2. We removed from this version the results related to chordal simplicial complexes. They will be included in the second paper