A. Lo

activity

20122019

k

-rainbow connected graphs

11 citations · 18 across the 3 of their papers we have counts for

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9 papers · 1 filter

math.CO2019

Decomposing tournaments into paths

Allan Lo, Viresh Patel, Jozef Skokan +1

We consider a generalisation of Kelly's conjecture which is due to Alspach, Mason, and Pullman from 1976. Kelly's conjecture states that every regular tournament has an edge decomp…

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

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

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…