Allan Lo

activity

20182025

collaborators

8 papers

math.CO2025

From finding a spanning subgraph $H$ to an $H$ -factor

Allan Lo

A typical Dirac-type problem in extremal graph theory is to determine the minimum degree threshold for a graph $G$ to have a spanning subgraph $H$ , e.g. the Dirac theorem. A natura…

math.CO2025

Embedding loose trees in $k$ -uniform hypergraphs

Yaobin Chen, Allan Lo

A classical result of Komlós, Sárközy and Szemerédi shows that every large $n$ -vertex graph with minimum degree at least $(1/2 + γ) n$ contains all spanning trees of bounded degree. W…

math.CO2024

Simultaneous edge-colourings

Simona Boyadzhiyska, Richard Lang, Allan Lo +1

We study a generalisation of Vizing's theorem, where the goal is to simultaneously colour the edges of graphs $G_{1}, \dots, G_{k}$ with few colours. We obtain asymptotically optimal bou…

math.CO2024

Complete tripartite subgraphs of balanced tripartite graphs with large minimum degree

Yihan Chen, Jialin He, Allan Lo +3

In 1975 Bollobás, Erdős, and Szemerédi asked what minimum degree guarantees an octahedral subgraph $K_{3} (2)$ in any tripartite graph $G$ with $n$ vertices in each vertex class. We s…

math.CO2024

Towards an edge-coloured Corrádi--Hajnal theorem

Allan Lo, Ella Williams

A classical result of Corrádi and Hajnal states that every graph $G$ on $n$ vertices with $n \in 3 N$ and $δ (G) \geq 2 n /3$ contains a perfect triangle-tiling, i.e.,\ a spanni…

math.CO2024

Polynomial bounds for monochromatic tight cycle partition in $r$ -edge-coloured $K_{n}^{(k)}$

Debmalya Bandyopadhyay, Allan Lo

Let $K_{n}^{(k)}$ be the complete $k$ -graph on $n$ vertices. A $k$ -uniform tight cycle is a $k$ -graph with its vertices cyclically ordered so that every $k$ consecutive vertices form…

math.CO2023

Ramsey goodness of $k$ -uniform paths, or the lack thereof

Simona Boyadzhiyska, Allan Lo

Given a pair of $k$ -uniform hypergraphs $(G, H)$ , the Ramsey number of $(G, H)$ , denoted by $R (G, H)$ , is the smallest integer $n$ such that in every red/blue-colouring of the edges o…

math.CO2018

Codegree Turán density of complete $r$ -uniform hypergraphs

Allan Lo, Yi Zhao

Let $r \geq 3$ . Given an $r$ -graph $H$ , the minimum codegree $δ_{r - 1} (H)$ is the largest integer $t$ such that every $(r - 1)$ -subset of $V (H)$ is contained in at least $t$ edges of $H…

From finding a spanning subgraph H to an H-factor

Embedding loose trees in k-uniform hypergraphs

Simultaneous edge-colourings

Complete tripartite subgraphs of balanced tripartite graphs with large minimum degree

Towards an edge-coloured Corrádi--Hajnal theorem

Polynomial bounds for monochromatic tight cycle partition in r-edge-coloured Kn(k)​

Ramsey goodness of k-uniform paths, or the lack thereof

Codegree Turán density of complete r-uniform hypergraphs

From finding a spanning subgraph $H$ to an $H$ -factor

Embedding loose trees in $k$ -uniform hypergraphs

Polynomial bounds for monochromatic tight cycle partition in $r$ -edge-coloured $K_{n}^{(k)}$

Ramsey goodness of $k$ -uniform paths, or the lack thereof

Codegree Turán density of complete $r$ -uniform hypergraphs