A. Lo

activity

20102023

most citedEdge-decompositions of graphs with high minimum degree

64 citations · 285 across the 44 of their papers we have counts for

collaborators

Showing 2018Show all

5 papers · 1 filter

math.CO2018

Long properly coloured cycles in edge-coloured graphs

Allan Lo

Let $G$ be an edge-coloured graph. The minimum colour degree $δ^{c} (G)$ of $G$ is the largest integer $k$ such that, for every vertex $v$ , there are at least $k$ distinct colours on…

math.CO2018

Minimalist designs

Ben Barber, Stefan Glock, Daniela Kühn +3

The iterative absorption method has recently led to major progress in the area of (hyper-)graph decompositions. Amongst other results, a new proof of the Existence conjecture for c…

math.CO2018

Density of monochromatic infinite paths

Allan Lo, Nicolás Sanhueza-Matamala, Guanghui Wang

For any subset $A \subseteq N$ , we define its upper density to be $lim sup_{n \to \infty} ∣ A \cap {1, \dots, n} ∣/ n$ . We prove that every $2$ -edge-colourin…

math.CO2018★ 3 cited

Monochromatic cycle partitions in random graphs

Richard Lang, Allan Lo

Erdős, Gyárfás and Pyber showed that every $r$ -edge-coloured complete graph $K_{n}$ can be covered by $25 r^{2} lo g r$ vertex-disjoint monochromatic cycles (independent of $n$ ). Here,…

math.CO2018★ 1 cited

On a conjecture of Erdős on locally sparse Steiner triple systems

Stefan Glock, Daniela Kühn, Allan Lo +1

A famous theorem of Kirkman says that there exists a Steiner triple system of order $n$ if and only if $n \equiv 1, 3 mod 6$ . In 1973, Erdős conjectured that one can find so-called…