New Bounds for Zarankiewicz Numbers via Reinforced LLM Evolutionary Search

ArXi:2605.01120v1 Announce Type: new The Zarankiewicz number $\textbf{Z}(m, n, s, t)$ is the maximum number of edges in a bipartite graph $G_{m, n}$ such that there is no complete $K_{s, t}$ bipartite subgraph. We determine for the first time the exact values of three Zarankiewicz numbers: $\textbf{Z}(11, 21, 3, 3)=116$, $\textbf{Z}(11, 22, 3, 3)=121$, and $\textbf{Z}(12, 22, 3, 3)=132$. We further establish lower bounds for 41 Zarankiewicz numbers, including several that are within one edge of the best known upper bound, and we match the established value in four closed cases.