Allan Lo

collaborators

5 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…

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

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

Embedding loose trees in $k$ -uniform hypergraphs