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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2102.07894 |
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| _version_ | 1866915335516454912 |
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| author | Grinberg, Darij Katthän, Lukas Lewis, Joel Brewster |
| author_facet | Grinberg, Darij Katthän, Lukas Lewis, Joel Brewster |
| contents | We study two simplicial complexes arising from a directed graph $G = (V, E)$ with two chosen vertices $s$ and $t$: the *path-free complex*, consisting of all subsets $F \subseteq E$ that contain no path from $s$ to $t$, and the *path-missing complex*, its Alexander dual. Using discrete Morse theory, we prove that both complexes have well-behaved homotopy types -- either contractible or homotopy-equivalent to spheres. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2102_07894 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | The path-missing and path-free complexes of a directed graph Grinberg, Darij Katthän, Lukas Lewis, Joel Brewster Combinatorics Algebraic Topology 05E45, 05C21, 05C31, 05A19 We study two simplicial complexes arising from a directed graph $G = (V, E)$ with two chosen vertices $s$ and $t$: the *path-free complex*, consisting of all subsets $F \subseteq E$ that contain no path from $s$ to $t$, and the *path-missing complex*, its Alexander dual. Using discrete Morse theory, we prove that both complexes have well-behaved homotopy types -- either contractible or homotopy-equivalent to spheres. |
| title | The path-missing and path-free complexes of a directed graph |
| topic | Combinatorics Algebraic Topology 05E45, 05C21, 05C31, 05A19 |
| url | https://arxiv.org/abs/2102.07894 |