Daniel Horsley

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math.CO2025

Improved upper bounds on Zarankiewicz numbers

Sara Davies, Peter Gill, Daniel Horsley

For positive integers $s, t, m$ and $n$ , the Zarankiewicz number $z (m, n; s, t)$ is the maximum number of edges in a subgraph of $K_{m, n}$ that has no complete bipartite subgraph contai…

math.CO2024

Zarankiewicz numbers near the triple system threshold

Guangzhou Chen, Daniel Horsley, Adam Mammoliti

For positive integers $m$ and $n$ , the Zarankiewicz number $Z_{2, 2} (m, n)$ can be defined as the maximum total degree of a linear hypergraph with $m$ vertices and $n$ edges. Guy det…