Jane Tan

activity

20232026

collaborators

11 papers

math.CO2026

Hypergraphs with the smallest Hall ratio are still hard to colour

Veronica Bitonti, Freddie Illingworth, Pedram Noohi +1

For $H$ a hypergraph, the Hall ratio $ρ (H) = max_{X \subseteq V (H)} \frac{∣ X ∣}{α ( H [ X ])}$ is a natural lower bound for its chromatic number, and among non-empty $k$ -u…

math.CO2026

Two Relaxations of the Dominating Hadwiger's Conjecture

António Girão, Sergey Norin, Youri Tamitegama +1

Illingworth and Wood recently proposed the Dominating Hadwiger's Conjecture, a strengthening of Hadwiger's Conjecture which asserts that every graph with no dominating $K_{t}$ -model…

math.CO2026

The Dominating 4-Colour Theorem

António Girão, Freddie Illingworth, Bojan Mohar +6

A "dominating $K_{t}$ -model" in a graph $G$ is a sequence $(T_{1}, \dots, T_{t})$ of pairwise vertex-disjoint connected subgraphs of $G$ , such that whenever $1 \leq i < j \leq t$ every vertex…

math.CO2026

Canonical labelling of random regular graphs

Mikhail Isaev, Tamás Makai, Brendan McKay +3

We prove that whenever $d = d (n) \to \infty$ and $n - d \to \infty$ as $n \to \infty$ , then with high probability for any non-trivial initial colouring, the colour refinement algorithm disti…

math.CO2025

Packing subdivisions into regular graphs

Richard Montgomery, Kalina Petrova, Arjun Ranganathan +1

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

math.CO2025

A local limit theorem for the edge counts of random induced subgraphs of a random graph

Paul Balister, Emil Powierski, Alex Scott +1

Consider a `dense' Erdős--Rényi random graph model $G = G_{n, M}$ with $n$ vertices and $M$ edges, where we assume the edge density $M / (2 n)$ is bounded away from 0 and 1. Fix…

math.CO2025

Tight Bounds for Hypercube Minor-Universality

Emma Hogan, Lukas Michel, Alex Scott +3

Benjamini, Kalifa and Tzalik recently proved that there is an absolute constant $c > 0$ such that any graph with at most $c \cdot 2^{d} / d$ edges and no isolated vertices is a minor of th…

math.CO2024

Clustered Colouring of Graph Products

Rutger Campbell, J. Pascal Gollin, Kevin Hendrey +5

A colouring of a graph $G$ has clustering $k$ if the maximum number of vertices in a monochromatic component equals $k$ . Motivated by recent results showing that many natural graph…

math.CO2024

When $t$ -intersecting hypergraphs admit bounded $c$ -strong colourings

Kevin Hendrey, Freddie Illingworth, Nina Kamčev +1

The $c$ -strong chromatic number of a hypergraph is the smallest number of colours needed to colour its vertices so that every edge sees at least $c$ colours or is rainbow. We show…

math.CO2024

A note on graphs of $k$ -colourings

Emma Hogan, Alex Scott, Youri Tamitegama +1

For a graph $G$ , the $k$ -colouring graph of $G$ has vertices corresponding to proper $k$ -colourings of $G$ and edges between colourings that differ at a single vertex. The graph su…

math.CO2023

Boundary rigidity of 3D CAT(0) cube complexes

John Haslegrave, Alex Scott, Youri Tamitegama +1

The boundary rigidity problem is a classical question from Riemannian geometry: if $(M, g)$ is a Riemannian manifold with smooth boundary, is the geometry of $M$ determined up to i…

Hypergraphs with the smallest Hall ratio are still hard to colour

Two Relaxations of the Dominating Hadwiger's Conjecture

The Dominating 4-Colour Theorem

Canonical labelling of random regular graphs

Packing subdivisions into regular graphs

A local limit theorem for the edge counts of random induced subgraphs of a random graph

Tight Bounds for Hypercube Minor-Universality

Clustered Colouring of Graph Products

When t-intersecting hypergraphs admit bounded c-strong colourings

A note on graphs of k-colourings

Boundary rigidity of 3D CAT(0) cube complexes

When $t$ -intersecting hypergraphs admit bounded $c$ -strong colourings

A note on graphs of $k$ -colourings