Zach Hunter

activity

20232026

K_{s, s}

-free graphs with polynomial average degree

2 citations · 2 across the 19 of their papers we have counts for

collaborators

Showing 2024Show all

7 papers · 1 filter

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 $…

math.CO2024

Disjoint pairs in set systems and combinatorics of low rank matrices

Zach Hunter, Aleksa Milojević, Benny Sudakov +1

We study and solve several problems in two closely related settings: set families in $2^{[n]}$ with many disjoint pairs of sets and low rank matrices with many zero entries. - More…

math.CO2024

Long induced paths in $K_{s, s}$ -free graphs

Zach Hunter, Aleksa Milojević, Benny Sudakov +1

More than 40 years ago, Galvin, Rival and Sands showed that every $K_{s, s}$ -free graph containing an $n$ -vertex path must contain an induced path of length $f (n)$ , where $f(n)\to…

math.CO2024

Blowups of triangle-free graphs

António Girão, Zach Hunter, Yuval Wigderson

A highly influential result of Nikiforov states that if an $n$ -vertex graph $G$ contains at least $γ n^{h}$ copies of a fixed $h$ -vertex graph $H$ , then $G$ contains a blowup of $H$ o…

math.NT2024

Improving Behrend's construction: Sets without arithmetic progressions in integers and over finite fields

Christian Elsholtz, Zach Hunter, Laura Proske +1

We prove new lower bounds on the maximum size of subsets $A \subseteq {1, \dots, N}$ or $A \subseteq F_{p}^{n}$ not containing three-term arithmetic progressions. In the setting…

math.CO2024

Induced Ramsey problems for trees and graphs with bounded treewidth

Zach Hunter, Benny Sudakov

The induced $q$ -color size-Ramsey number $r^_{ind} (H; q)$ of a graph $H$ is the minimal number of edges a host graph $G$ can have so that every $q$ -edge-coloring of $G$ …

math.CO2024

Kővári-Sós-Turán theorem for hereditary families

Zach Hunter, Aleksa Milojević, Benny Sudakov +1

The celebrated Kővári-Sós-Turán theorem states that any $n$ -vertex graph containing no copy of the complete bipartite graph $K_{s, s}$ has at most $O_{s} (n^{2 - 1/ s})$ edges. In the pas…

Monochromatic odd cycles in edge-coloured complete graphs

Disjoint pairs in set systems and combinatorics of low rank matrices

Long induced paths in Ks,s​-free graphs

Blowups of triangle-free graphs

Improving Behrend's construction: Sets without arithmetic progressions in integers and over finite fields

Induced Ramsey problems for trees and graphs with bounded treewidth

Kővári-Sós-Turán theorem for hereditary families

Long induced paths in $K_{s, s}$ -free graphs