Line graphs of simplicial complexes
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866909787239743488 |
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| author | Olteanu, Anda |
| author_facet | Olteanu, Anda |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_13463 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Line graphs of simplicial complexes Olteanu, Anda Commutative Algebra Combinatorics 13A02, 05E40 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. |
| title | Line graphs of simplicial complexes |
| topic | Commutative Algebra Combinatorics 13A02, 05E40 |
| url | https://arxiv.org/abs/2206.13463 |