Allan Lo

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math.CO2023

Cycle Partitions in Dense Regular Digraphs and Oriented Graphs

Allan Lo, Viresh Patel, Mehmet Akif Yıldız

A conjecture of Jackson from 1981 states that every $d$ -regular oriented graph on $n$ vertices with $n \leq 4 d + 1$ is Hamiltonian. We prove this conjecture for sufficiently large $n$ …

math.CO2023

Almost partitioning every $2$ -edge-coloured complete $k$ -graph into $k$ monochromatic tight cycles

Allan Lo, Vincent Pfenninger

A $k$ -uniform tight cycle is a $k$ -graph with a cyclic order of its vertices such that every $k$ consecutive vertices from an edge. We show that for $k \geq 3$ , every red-blue edge-…

math.CO2019

Transitive tournament tilings in oriented graphs with large minimum total degree

Louis DeBiasio, Allan Lo, Theodore Molla +1

Let $T_{k}$ be the transitive tournament on $k$ vertices. We show that every oriented graph on $n = 4 m$ vertices with minimum total degree $(11/12 + o (1)) n$ can be partitioned into…

Cycle Partitions in Dense Regular Digraphs and Oriented Graphs

Almost partitioning every 2-edge-coloured complete k-graph into k monochromatic tight cycles

Transitive tournament tilings in oriented graphs with large minimum total degree

Almost partitioning every $2$ -edge-coloured complete $k$ -graph into $k$ monochromatic tight cycles