Zach Hunter

activity

20242026

collaborators

8 papers

math.CO2026

Large point-line matchings and small Nikodym sets

Zach Hunter, Cosmin Pohoata, Jacques Verstraete +1

For any integer $d \geq 2$ and prime power $q$ , we construct unexpectedly large induced matchings in the point-line incidence graph of $F_{q}^{d}$ by leveraging a new conn…

math.CO2025

Cyclic subsets of tournaments

Zach Hunter, Teng Liu, Aleksa Milojević +1

Let $G$ be a Dirac graph, and let $S$ be a vertex subset of $G$ , chosen uniformly at random. How likely is the induced subgraph $G [S]$ to be Hamiltonian? This question, proposed by…

math.CO2025

An improved construction for the triangle removal lemma

Zach Hunter

We construct $n$ -vertex graphs $G$ where $ε n^{2}$ edges must be deleted to become triangle-free, which contain less than $ε^{(C_{new} - o (1)) l o g_{2} 1/ ε} n^{3}$ triangles for $C_{\t…

math.CO2025

$C_{4}$ -free subgraphs of high degree with geometric applications

Zach Hunter, Aleksa Milojević, Istvan Tomon +1

The Zarankiewicz problem, a cornerstone problem in extremal graph theory, asks for the maximum number of edges in an $n$ -vertex graph that does not contain the complete bipartite g…

math.CO2025

Lower bounds for Ramsey numbers of bounded degree hypergraphs

Domagoj Bradač, Zach Hunter, Benny Sudakov

We prove that, for all $k \geq 3,$ and any integers $Δ, n$ with $n \geq Δ,$ there exists a $k$ -uniform hypergraph on $n$ vertices with maximum degree at most $Δ$ whose $4$ -color Rams…

math.CO2024

Monochromatic odd cycles in edge-coloured complete graphs

António Girão, Zach Hunter

It is easy to see that every $q$ -edge-colouring of the complete graph on $2^{q} + 1$ vertices must contain a monochromatic odd cycle. A natural question raised by Erdős and Graham in $…

Large point-line matchings and small Nikodym sets

Cyclic subsets of tournaments

An improved construction for the triangle removal lemma

C4​-free subgraphs of high degree with geometric applications

Lower bounds for Ramsey numbers of bounded degree hypergraphs

Monochromatic odd cycles in edge-coloured complete graphs

$C_{4}$ -free subgraphs of high degree with geometric applications