Topology of Cut Complexes II
Combinatorics
2025-09-09 v1 Algebraic Topology
Abstract
We continue the study of the -cut complex of a graph 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 - and -polynomials of the cut complex of the disjoint union of two graphs and , and for the homology representation of . 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.
Cite
@article{arxiv.2407.08158,
title = {Topology of Cut Complexes II},
author = {Margaret Bayer and Mark Denker and Marija Jelić Milutinović and Sheila Sundaram and Lei Xue},
journal= {arXiv preprint arXiv:2407.08158},
year = {2025}
}
Comments
29 pages, 7 figures, 3 tables