Jane Tan

activity

20232026

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Showing 2026 · math.COShow all

4 papers · 2 filters

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…