Total Cut Complexes of Graphs
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866908522883579904 |
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| author | Bayer, Margaret Denker, Mark Milutinović, Marija Jelić Rowlands, Rowan Sundaram, Sheila Xue, Lei |
| author_facet | Bayer, Margaret Denker, Mark Milutinović, Marija Jelić Rowlands, Rowan Sundaram, Sheila Xue, Lei |
| contents | Inspired by work of Fröberg (1990), and Eagon and Reiner (1998), we define the \emph{total $k$-cut complex} of a graph $G$ to be the simplicial complex whose facets are the complements of independent sets of size $k$ in $G$. We study the homotopy types and combinatorial properties of total cut complexes for various families of graphs, including chordal graphs, cycles, bipartite graphs, the prism $K_n \times K_2$, and grid graphs, using techniques from algebraic topology and discrete Morse theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_13503 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Total Cut Complexes of Graphs Bayer, Margaret Denker, Mark Milutinović, Marija Jelić Rowlands, Rowan Sundaram, Sheila Xue, Lei Combinatorics Algebraic Topology 57M15, 57Q70, 05C69, 05E45 Inspired by work of Fröberg (1990), and Eagon and Reiner (1998), we define the \emph{total $k$-cut complex} of a graph $G$ to be the simplicial complex whose facets are the complements of independent sets of size $k$ in $G$. We study the homotopy types and combinatorial properties of total cut complexes for various families of graphs, including chordal graphs, cycles, bipartite graphs, the prism $K_n \times K_2$, and grid graphs, using techniques from algebraic topology and discrete Morse theory. |
| title | Total Cut Complexes of Graphs |
| topic | Combinatorics Algebraic Topology 57M15, 57Q70, 05C69, 05E45 |
| url | https://arxiv.org/abs/2209.13503 |