Minimal Free Resolutions of Edge Ideals of Edge-Weighted Complete Bipartite Graphs
Bethany Kubik, Denise Rangel Tracy, Keri Ann Sather-Wagstaff
TL;DR
This paper provides explicit cellular minimal free resolutions for edge ideals of weighted complete bipartite graphs, extending Visscher's construction to characterize when it provides minimal resolutions.
Contribution
It explicitly describes cellular minimal free resolutions for edge ideals of weighted complete bipartite graphs and characterizes graphs where Visscher's construction is minimal.
Findings
Visscher's construction minimally resolves all edge ideals of undirected vertex-weighted complete bipartite graphs.
Characterization of edge-weighted complete bipartite graphs with minimal resolutions via Visscher's construction.
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.
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Taxonomy
TopicsRings, Modules, and Algebras · Commutative Algebra and Its Applications · Advanced Topology and Set Theory