Richard Montgomery

collaborators

6 papers

math.CO2026

A proof of Andersen's rainbow path conjecture for large $n$

Candida Bowtell, Richard Montgomery, Alp Müyesser +1

We show that, for sufficiently large $n$ , every properly edge-coloured $n$ -vertex complete graph contains a path with $n - 1$ vertices which uses each colour at most once (that is, a…

math.CO2026

Recent progress in graph theory using expansion

Richard Montgomery

Graph expansion has long been recognised as an important and desirable property with applications in a wide range of areas in computer science and mathematics. A particular form of…

math.CO2026

Nearly-uniform degree distributions in spanning subgraphs

Richard Montgomery, Alexey Pokrovskiy, Benny Sudakov

We show that, when $d = o (n)$ , every $d$ -regular $n$ -vertex graph contains a spanning subgraph whose degree distribution is nearly uniform, i.e., for each $0 \leq i \leq d$ , there are…

math.CO2026

On decomposition thresholds for odd-length cycles and other tripartite graphs

Darryn Bryant, Peter Dukes, Daniel Horsley +2

An (edge) decomposition of a graph $G$ is a set of subgraphs of $G$ whose edge sets partition the edge set of $G$ . Here we show, for each odd $ℓ \geq 5$ , that any graph $G$ of s…

math.CO2026

Packing subdivisions into regular graphs

Richard Montgomery, Kalina Petrova, Arjun Ranganathan +1

We show that, for any graph $F$ and $I^\cdot > 0$ , there exists a $d_{0} = d_{0} (F, I^\cdot)$ such that every $n$ -vertex $d$ -regular graph with $d \geq d_{0}$ has a collection of vertex-disjoint $F$ -su…

math.CO2025

Regular subgraphs at every density

Debsoumya Chakraborti, Oliver Janzer, Abhishek Methuku +1

In 1975, ErdÅs and Sauer asked to estimate, for any constant $r$ , the maximum number of edges an $n$ -vertex graph can have without containing an $r$ -regular subgraph. In a recent…

A proof of Andersen's rainbow path conjecture for large n

Recent progress in graph theory using expansion

Nearly-uniform degree distributions in spanning subgraphs

On decomposition thresholds for odd-length cycles and other tripartite graphs

Packing subdivisions into regular graphs

Regular subgraphs at every density

A proof of Andersen's rainbow path conjecture for large $n$