Minimal Free Resolutions of Edge Ideals of Edge-Weighted Complete Bipartite Graphs
Commutative Algebra
2024-07-02 v1
Abstract
We explicitly describe cellular minimal free resolutions of certain classes of edge ideals of weighted complete bipartite graphs based on a construction of Visscher. Specifically, we show that Visscher's construction minimally resolves all edge ideals of undirected vertex-weighted complete bipartite graphs, and we characterize the edge-weighted complete bipartite graphs whose edge ideals are minimally resolved by Visscher's construction.
Keywords
Cite
@article{arxiv.2407.00546,
title = {Minimal Free Resolutions of Edge Ideals of Edge-Weighted Complete Bipartite Graphs},
author = {Bethany Kubik and Denise Rangel Tracy and Keri Ann Sather-Wagstaff},
journal= {arXiv preprint arXiv:2407.00546},
year = {2024}
}