Paul Horn

collaborators

4 papers

math.CO2026

A short proof that $R (3, k) = Θ (k^{2} / lo g k)$

Samuel Harris, Zion Hefty, Paul Horn +2

We give a nibble-free construction proving $R (3, k) \geq (1/200 + o (1)) k^{2} / lo g k$ . We also include Shearer's proof bounding the independence number of a triangle-free graph, which impli…

math.CO2026

Subsequence sums in permutations

Collier Gaiser, Paul Horn

A sequence of positive integers $(a_{1}, a_{2}, \dots, a_{k})$ is called $ℓ$ -additive if $a_{1} + a_{2} + \dots + a_{k} = ℓ a_{1}$ or $ℓ a_{k}$ . In this paper, we prove that for all $k \geq 3$ , if $…

math.CO2026

On fixing and distinguishing numbers of trees

Calum Buchanan, Peter Dankelmann, Isabel Harris +3

A graph $G$ is $D$ -distinguishable if there is a labeling of its vertices with $D$ labels such that the only automorphism of $G$ which preserves the labeling is the identity. The d…

math.CO2025

Improving $R (3, k)$ in just two bites

Zion Hefty, Paul Horn, Dylan King +1

We present a flexible random construction which, for certain graphs $H$ , is able to produce $H$ -free graphs with edge density strictly larger than that of the $H$ -free process, whi…

A short proof that R(3,k)=Θ(k2/logk)

Subsequence sums in permutations

On fixing and distinguishing numbers of trees

Improving R(3,k) in just two bites

A short proof that $R (3, k) = Θ (k^{2} / lo g k)$

Improving $R (3, k)$ in just two bites