A. Scott

activity

20062026

most citedMonochromatic cycles and the monochromatic circumference in 2-coloured graphs

5 citations · 15 across the 14 of their papers we have counts for

collaborators

Showing 2023Show all

5 papers · 1 filter

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

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

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

Tung Nguyen, Alex Scott, Paul Seymour

Erdős and Hajnal conjectured that for every graph $H$ , there exists $c > 0$ such that every $H$ -free graph $G$ has a clique or a stable set of size at least $∣ G ∣^{c}$ (a graph is $H$ -f…

math.CO2023

Induced subgraph density. III. Cycles and subdivisions

Tung Nguyen, Alex Scott, Paul Seymour

We show that for every two cycles $C, D$ , there exists $c > 0$ such that if $G$ is both $C$ -free and $D$ -free then $G$ has a clique or stable set of size at least $∣ G ∣^{c}$ .…

math.CO2023

Induced subgraph density. II. Sparse and dense sets in cographs

Jacob Fox, Tung Nguyen, Alex Scott +1

A well-known theorem of Rödl says that for every graph $H$ , and every $ε > 0$ , there exists $δ > 0$ such that if $G$ does not contain an induced copy of $H$ , then there exists $X\subse…

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

Induced C4​-free subgraphs with large average degree

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

Induced subgraph density. III. Cycles and subdivisions

Induced subgraph density. II. Sparse and dense sets in cographs

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