Topology of Cut Complexes II
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866909775193702400 |
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| author | Bayer, Margaret Denker, Mark Milutinović, Marija Jelić Sundaram, Sheila Xue, Lei |
| author_facet | Bayer, Margaret Denker, Mark Milutinović, Marija Jelić Sundaram, Sheila Xue, Lei |
| contents | We continue the study of the $k$-cut complex $Δ_k(G)$ of a graph $G$ initiated in the paper of Bayer, Denker, Jelić Milutinović, Rowlands, Sundaram and Xue [Topology of cut complexes of graphs, SIAM J. on Discrete Math. 38(2): 1630--1675 (2024)].
We give explicit formulas for the $f$- and $h$-polynomials of the cut complex $Δ_k(G_1+G_2) $ of the disjoint union of two graphs $G_1$ and $G_2$, and for the homology representation of $Δ_k(K_m+K_n)$.
We also study the cut complex of the squared path and the grid graph. Our techniques include tools from combinatorial topology, discrete Morse theory and equivariant poset topology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_08158 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Topology of Cut Complexes II Bayer, Margaret Denker, Mark Milutinović, Marija Jelić Sundaram, Sheila Xue, Lei Combinatorics Algebraic Topology We continue the study of the $k$-cut complex $Δ_k(G)$ of a graph $G$ initiated in the paper of Bayer, Denker, Jelić Milutinović, Rowlands, Sundaram and Xue [Topology of cut complexes of graphs, SIAM J. on Discrete Math. 38(2): 1630--1675 (2024)]. We give explicit formulas for the $f$- and $h$-polynomials of the cut complex $Δ_k(G_1+G_2) $ of the disjoint union of two graphs $G_1$ and $G_2$, and for the homology representation of $Δ_k(K_m+K_n)$. We also study the cut complex of the squared path and the grid graph. Our techniques include tools from combinatorial topology, discrete Morse theory and equivariant poset topology. |
| title | Topology of Cut Complexes II |
| topic | Combinatorics Algebraic Topology |
| url | https://arxiv.org/abs/2407.08158 |