Total Cut Complexes of Graphs
Combinatorics
2025-09-09 v2 Algebraic Topology
Abstract
Inspired by work of Fr\"oberg (1990), and Eagon and Reiner (1998), we define the \emph{total -cut complex} of a graph to be the simplicial complex whose facets are the complements of independent sets of size in . We study the homotopy types and combinatorial properties of total cut complexes for various families of graphs, including chordal graphs, cycles, bipartite graphs, the prism , and grid graphs, using techniques from algebraic topology and discrete Morse theory.
Cite
@article{arxiv.2209.13503,
title = {Total Cut Complexes of Graphs},
author = {Margaret Bayer and Mark Denker and Marija Jelić Milutinović and Rowan Rowlands and Sheila Sundaram and Lei Xue},
journal= {arXiv preprint arXiv:2209.13503},
year = {2025}
}
Comments
25 pages, 2 figures, 3 tables. Minor revisions per referee comments. To appear in Discrete and Computational Geometry