R. Montgomery

activity

20232025

collaborators

4 papers

math.CO2025

Ramsey numbers of trees

Richard Montgomery, Matías Pavez-Signé, Jun Yan

We show that there exists a constant $c > 0$ such that every $n$ -vertex tree $T$ with $Δ (T) \leq c n$ has Ramsey number $R (T) = max {t_{1} + 2 t_{2}, 2 t_{1}} - 1$ , where $t_{1} \geq t_{2}$ are the sizes…

math.CO2024

Global rigidity of random graphs in $R$

Richard Montgomery, Rajko Nenadov, Julien Portier +1

We investigate the problem of reconstructing a set $P \subseteq R$ of distinct points, where the only information available about $P$ consists of the distances between some…

math.CO2023

Ramsey numbers of bounded degree trees versus general graphs

Richard Montgomery, Matías Pavez-Signé, Jun Yan

For every $k \geq 2$ and $Δ$ , we prove that there exists a constant $C_{Δ, k}$ such that the following holds. For every graph $H$ with $χ (H) = k$ and every tree with at least $C_{Δ,k}|H…

math.CO2023

Counting spanning subgraphs in dense hypergraphs

Richard Montgomery, Matías Pavez-Signé

We give a simple method to estimate the number of distinct copies of some classes of spanning subgraphs in hypergraphs with high minimum degree. In particular, for each $k \geq 2$ a…

Ramsey numbers of trees

Global rigidity of random graphs in R

Ramsey numbers of bounded degree trees versus general graphs

Counting spanning subgraphs in dense hypergraphs

Global rigidity of random graphs in $R$