Tony Huynh

activity

20242026

collaborators

5 papers

math.CO2026

The ErdÅs-PÃ³sa property for prime-length cycles fails (and beyond)

Maximilian Gorsky, Kevin Hendrey, Tony Huynh

We prove that for every $t \in N$ , prime-length cycles do not have the $\frac{1}{t}$ -integral ErdÅs-PÃ³sa property, even when restricted to planar graphs. We in fact prov…

math.CO2026

Stable cuts, NAC-colourings and flexible realisations of graphs

Katie Clinch, DÃ¡niel GaramvÃ¶lgyi, John Haslegrave +3

A (2-dimensional) realisation of a graph $G$ is a pair $(G, p)$ , where $p$ maps the vertices of $G$ to $R^{2}$ . A realisation is flexible if it can be continuously deformed w…

math.CO2025

Triangulated spheres with holes in triangulated surfaces

Katie Clinch, Sean Dewar, Niloufar Fuladi +6

Let $S_{h}$ denote a sphere with $h$ holes. Given a triangulation $G$ of a surface $M$ , we consider the question of when $G$ contains a spanning subgraph $H$ such t…

math.CO2025

Sharp thresholds for NAC-colourings and stable cuts in random graphs

Katie Clinch, John Haslegrave, Tony Huynh +1

NAC-colourings of graphs correspond to flexible quasi-injective realisations in $R^{2}$ . A special class of NAC-colourings are those that arise from stable cuts. We give s…

math.CO2024

Constructions, bounds, and algorithms for peaceable queens

Katie Clinch, Matthew Drescher, Tony Huynh +1

The peaceable queens problem asks to determine the maximum number $a (n)$ such that there is a placement of $a (n)$ white queens and $a (n)$ black queens on an $n \times n$ chessboard…

The ErdÅs-PÃ³sa property for prime-length cycles fails (and beyond)

Stable cuts, NAC-colourings and flexible realisations of graphs

Triangulated spheres with holes in triangulated surfaces

Sharp thresholds for NAC-colourings and stable cuts in random graphs

Constructions, bounds, and algorithms for peaceable queens

The ErdÅs-PÃ³sa property for prime-length cycles fails (and beyond)