Richard Lang

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math.CO2026

Monochromatic cycle partitions in 3-mean edge-colourings

Richard Lang, Guilherme Oliveira Mota

Given $r \in N$ and an edge-coloured complete graph such that the average number of colours incident with a vertex is at most $r$ , Conlon and Stein asked whether there is…

math.CO2026

Dirac subgraphs of powers of cycles are Hamiltonian

Richard Lang, Alp Müyesser, Mathias Schacht +1

We show that, for every $ε > 0$ and all sufficiently large $k$ , any spanning subgraph of the $k$ th power of a cycle with minimum degree at least $(1 + ε) k$ contains…

math.CO2024

Tight Hamiltonicity from dense links of triples

Richard Lang, Mathias Schacht, Jan Volec

We show that for all $k \geq 4$ , $ε > 0$ , and $n$ sufficiently large, every $k$ -uniform hypergraph on $n$ vertices in which each set of $k - 3$ vertices is contained in at le…

math.CO2023

Resilience for Loose Hamilton Cycles

José D. Alvarado, Yoshiharu Kohayakawa, Richard Lang +2

We study the emergence of loose Hamilton cycles in subgraphs of random hypergraphs. Our main result states that the minimum $d$ -degree threshold for loose Hamiltonicity relative to…