Topology of Cut Complexes of Graphs
| Autor: | Bayer, Margaret, Denker, Mark, Milutinović, Marija Jelić, Rowlands, Rowan, Sundaram, Sheila, Xue, Lei |
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| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | SIAM J. on Discrete Mathematics,Vol. 38 (2), 1630--1675 (2024) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1137/23M1569034 |
| Popis: | We define the $k$-cut complex of a graph $G$ with vertex set $V(G)$ to be the simplicial complex whose facets are the complements of sets of size $k$ in $V(G)$ inducing disconnected subgraphs of $G$. This generalizes the Alexander dual of a graph complex studied by Fr\"oberg (1990), and Eagon and Reiner (1998). We describe the effect of various graph operations on the cut complex, and study its shellability, homotopy type and homology for various families of graphs, including trees, cycles, complete multipartite graphs, and the prism $K_n \times K_2$, using techniques from algebraic topology, discrete Morse theory and equivariant poset topology. Comment: 37 pages, 10 figures, 1 table, final version incorporating referees' comments. To appear in SIAM Journal on Discrete Mathematics |
| Databáze: | arXiv |
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