Emma Hogan

activity

20242026

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6 papers · 1 filter

math.CO2026

Sharp bounds for covering with large cliques and independent sets

Veronica Bitonti, Emma Hogan, Tommy Walker Mackay

Let $n (k_{1}, k_{2})$ be the least integer $n$ such that there exists a graph on $n$ vertices in which every vertex is contained in both a clique of size $k_{1}$ and an independent set o…

math.CO2026

Colour-balanced subgraphs

Emma Hogan, Alex Scott, Dmitry Tsarev

A $k$ -edge-coloured graph is colour-balanced if each colour appears equally often. Resolving a conjecture of Pardey and Rautenbach, we show that any colour-balanced $k$ -edge-colour…

math.CO2025

Infinite Schnyder Woods

Louigi Addario-Berry, Emma Hogan, Lukas Michel +1

It is well-known that any finite triangulation possesses a unique maximal Schnyder wood. We introduce Schnyder woods of infinite triangulations, and prove there exists a unique max…

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

Exponential odd-distance sets under the Manhattan metric

Alberto Espuny Díaz, Emma Hogan, Freddie Illingworth +3

We construct a set of $2^{n}$ points in $R^{n}$ such that all pairwise Manhattan distances are odd integers, which improves the recent linear lower bound of Golovanov, Kupavsk…

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…