The complete bipartite graph ideal degree conjecture

Let $K_{m,n}$ be the complete bipartite graph with parts of sizes $m$ and $n$, and let $I_{K_{m,n}}$ be its graph ideal. Here $\min\{m,n\}$ denotes the smaller part size.

Complete bipartite graph ideal degree conjecture. The graph ideal for $G=K_{m,n}$ is generated in degree at most

$$2^{\min\{m,n\}}.$$

This extends the established result for $K_{2,n}$; the paper notes that the conjecture is supported by the preceding result and remains unproved there.