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arXiv · 2407.08158

Topology of Cut Complexes II

Margaret Bayer·Mark Denker·Marija Jelić Milutinović·Sheila Sundaram·Lei Xue
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Abstract

We continue the study of the $k$-cut complex $\Delta_k(G)$ of a graph $G$ initiated in the paper of Bayer, Denker, Jeli\'c Milutinovi\'c, 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 $\Delta_k(G_1+G_2) $ of the disjoint union of two graphs $G_1$ and $G_2$, and for the homology representation of $\Delta_k(K_m+K_n)$. 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.

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Margaret Bayer, Mark Denker, Marija Jelić Milutinović, Sheila Sundaram, Lei Xue. 2024-07-11. Topology of Cut Complexes II. https://doi.org/10.1137/24m1676077

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