Allan Lo

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7 papers · 1 filter

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

Complete tripartite subgraphs of balanced tripartite graphs with large minimum degree

Yihan Chen, Jialin He, Allan Lo +3

In 1975 BollobÃ¡s, ErdÅs, and SzemerÃ©di asked what minimum degree guarantees an octahedral subgraph $K_{3} (2)$ in any tripartite graph $G$ with $n$ vertices in each vertex class. W…

math.CO2025

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.CO2025

Embedding loose trees in $k$ -uniform hypergraphs

Yaobin Chen, Allan Lo

A classical result of KomlÃ³s, SÃ¡rkÃ¶zy and SzemerÃ©di shows that every large $n$ -vertex graph with minimum degree at least $(1/2 + I^^{3}) n$ contains all spanning trees of bounded degr…

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

Towards an edge-coloured CorrÃ¡di--Hajnal theorem

Allan Lo, Ella Williams

A classical result of CorrÃ¡di and Hajnal states that every graph $G$ on $n$ vertices with $n \in 3 N$ and $I^´ (G) \geq 2 n /3$ contains a perfect triangle-tiling, i.e.,\ a span…

From finding a spanning subgraph H to an H-factor

Complete tripartite subgraphs of balanced tripartite graphs with large minimum degree

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

Embedding loose trees in k-uniform hypergraphs

Simultaneous edge-colourings

Towards an edge-coloured CorrÃ¡di--Hajnal theorem

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

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

Embedding loose trees in $k$ -uniform hypergraphs