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arXiv · 2512.24242

Spanning Components and Surfaces Under Minimum Vertex Degree

Jack Allsop·Ander Lamaison·Richard Lang·Silas Rathke
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Abstract

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 $G$ on $n$ vertices contains a spanning component if $\delta_1(G) \gtrsim \tfrac{1}{2} \binom{n}{2}$ and a spanning copy of any surface if $\delta_1(G) \gtrsim \tfrac{5}{9} \binom{n}{2}$, which in both cases is asymptotically optimal. This extends the work of Georgakopoulos, Haslegrave, Montgomery, and Narayanan who determined the corresponding minimum codegree conditions in this setting.

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Jack Allsop, Ander Lamaison, Richard Lang, Silas Rathke. 2025-12-30. Spanning Components and Surfaces Under Minimum Vertex Degree. https://arxiv.org/abs/2512.24242

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