Spanning spheres in Dirac hypergraphs
| Autor: | Illingworth, Freddie, Lang, Richard, Müyesser, Alp, Parczyk, Olaf, Sgueglia, Amedeo |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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 set of $k - 1$ vertices supported by an edge is contained in at least $n/2 + o(n)$ edges. This gives a topological extension of Dirac's theorem and asymptotically confirms a conjecture of Georgakopoulos, Haslegrave, Montgomery, and Narayanan. Unlike typical results in the area, our proof does not rely on the Absorption Method, the Regularity Lemma or the Blow-up Lemma. Instead, we use a recently introduced framework that is based on covering the vertex set of the host graph with a family of complete blow-ups. Comment: 20 pages |
| Databáze: | arXiv |
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