English

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}
}