Richard Lang

activity

20242026

collaborators

7 papers

math.CO2026

A hypergraph bandwidth theorem

Richard Lang, NicolÃ¡s Sanhueza-Matamala

A cornerstone of extremal graph theory due to ErdÅs and Stone states that the edge density which guarantees a fixed graph $F$ as subgraph also asymptotically guarantees a blow-up…

math.CO2025

Spanning Components and Surfaces Under Minimum Vertex Degree

Jack Allsop, Ander Lamaison, Richard Lang +1

We study minimum vertex-degree conditions in 3-uniform hypergraphs for (tight) spanning components and (combinatorial) surfaces. Our main results show that a 3-uniform hypergraph $…

math.CO2025

Blowing up Dirac's theorem

Richard Lang, NicolÃ¡s Sanhueza-Matamala

We show that every graph $G$ on $n$ vertices with $I^´ (G) \geq (1/2 + ε) n$ is spanned by a complete blow-up of a cycle with clusters of nearly uniform size $I^c ◯ (lo g n)$ . The…

math.CO2025

Loose Hamiltonicity

Richard Lang, NicolÃ¡s Sanhueza-Matamala

We study the appearance of Hamilton $ℓ$ -cycles in dense $k$ -uniform hypergraphs when $ℓ \leq k - 2$ and $k - ℓ$ does not divide $k$ . Our main result reduces this problem to th…

math.CO2025

Colour-bias perfect matchings in hypergraphs

HiÃªp HÃ n, Richard Lang, JoÃ£o Pedro Marciano +4

We study conditions under which an edge-coloured hypergraph has a particular substructure that contains more than the trivially guaranteed number of monochromatic edges. Our main r…

math.CO2025

Spanning spheres in Dirac hypergraphs

Freddie Illingworth, Richard Lang, Alp MÃ¼yesser +2

We show that a $k$ -uniform hypergraph on $n$ vertices has a spanning subgraph homeomorphic to the $(k - 1)$ -dimensional sphere provided that $H$ has no isolated vertices and each s…