Minimal Free Resolutions of Edge Ideals of Edge-Weighted Complete Bipartite Graphs

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.