Richard Lang

collaborators

4 papers

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

Loose Hamiltonicity

Richard Lang, Nicolás 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.CO2024

Blowing up Dirac's theorem

Richard Lang, Nicolás Sanhueza-Matamala

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

math.CO2024

A hypergraph bandwidth theorem

Richard Lang, Nicolás Sanhueza-Matamala

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