Jane Tan

collaborators

6 papers

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

AntÃ³nio GirÃ£o, 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, TamÃ¡s 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.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

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' ErdÅs--RÃ©nyi 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. Fi…

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…