The graph minor theorem in topological combinatorics
Combinatorics
2023-04-17 v2 Commutative Algebra
Algebraic Topology
Abstract
We study a variety of natural constructions from topological combinatorics, including matching complexes as well as other graph complexes, from the perspective of the graph minor category of \parencite{MiProRa}. We prove that these complexes must have universally bounded torsion in their homology across all graphs of bounded genus. One may think of these results as arising from an algebraic version of the graph minor theorem of Robertson and Seymour \parencite{RSXX,RSXXIII}.
Keywords
Cite
@article{arxiv.2012.01679,
title = {The graph minor theorem in topological combinatorics},
author = {Dane Miyata and Eric Ramos},
journal= {arXiv preprint arXiv:2012.01679},
year = {2023}
}
Comments
Major Revision: Due to the gap found in the proof of the categorical graph minor theorem, this paper has been rewritten to prove a weaker version of that theorem. arXiv admin note: text overlap with arXiv:2004.05544