A. Scott

activity

20032026

most citedThe repulsive lattice gas, the independent-set polynomial, and the Lovász local lemma

203 citations · 470 across the 96 of their papers we have counts for

collaborators

138 papers

math.CO2026

A short proof of the Erd\H os--Sós Conjecture

Oliver Riordan, Alex Scott

The Erd\H os--Sós Conjecture was recently proved by GPT-6 Astra, using a very ingenious and surprising argument. In this note, we present a simplified version of this argument in a…

math.CO2026

Far-apart Erdős--Pósa property of long cycles

Maria Chudnovsky, Vida Dujmović, Gwenaël Joret +4

We prove that there exist functions $f : N^{2} \to N$ and $g : N \to N$ such that for all positive integers $k$ , $d$ , and $ℓ \geq 3$ , every graph $G$ either c…

math.CO2025

Infinite induced-saturated graphs

Marthe Bonamy, Carla Groenland, Tom Johnston +2

A graph $G$ is $H$ -induced-saturated if $G$ is $H$ -free but deleting any edge or adding any edge creates an induced copy of $H$ . There are non-trivial graphs $H$ , such as $P_{4}$ , fo…

math.CO2023

Induced subgraph density. V. All paths approach Erdos-Hajnal

Tung Nguyen, Alex Scott, Paul Seymour

The Erdős-Hajnal conjecture says that, for every graph $H$ , there exists $c > 0$ such that every $H$ -free graph on $n$ vertices has a clique or stable set of size at least $n^{c}$ . In…

math.CO2023★ 2 cited

Induced $C_{4}$ -free subgraphs with large average degree

Xiying Du, António Girão, Zach Hunter +2

We prove that there exists a constant $C$ so that, for all $s, k \in N$ , if $G$ has average degree at least $k^{C s^{3}}$ and does not contain $K_{s, s}$ as a subgraph then it…

math.CO2023★ 1 cited

Induced subgraph density. IV. New graphs with the Erdős-Hajnal property