Topology of Cut Complexes II
Margaret M. Bayer, Mark S. Denker, Marija Jelić Milutinović, Sheila Sundaram, Xue Lei · SIAM Journal on Discrete Mathematics · 2025
Abstract. We continue the study of the [Formula: see text]-cut complex [Formula: see text] of a graph [Formula: see text] initiated in the paper of Bayer et al. [ SIAM J. Discrete Math., 38 (2024), pp. 1630–1675]. We give explicit formulas for the [Formula: see text]- and [Formula: see text]-polynomials of the cut complex [Formula: see text] of the disjoint union of two graphs [Formula: see text] and [Formula: see text], and for the homology representation of [Formula: see text]. 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.