Total cut complexes and their duals
Combinatorics
2026-03-09 v2 Algebraic Topology
Abstract
We study the total cut complexes and their Alexander duals. The homotopy type of these complexes is calculated for de th power of a cycle with at least vertices where , solving part of a conjecture of Bayer, Denker, Milutinovi\'c, Rowlands, Sundaram and Xue. The homotopy type of the -total cut complex for any th power of a cycle with also is calculated, solving a conjecture of Chauhan, Shukla and Vinayak. We give some results about the connectivity. The homotopy type of the complexes for complete multipartite graph is determined. We also study the complexes of cartesian products of paths and of cartesian products of complete graphs for the total -cut complex.
Keywords
Cite
@article{arxiv.2602.21427,
title = {Total cut complexes and their duals},
author = {Andrés Carnero Bravo},
journal= {arXiv preprint arXiv:2602.21427},
year = {2026}
}