@inproceedings{5991063ac3b14df7ba243fbc2a02b231,

title = "Ramsey Properties of Randomly Perturbed Hypergraphs",

abstract = "We study Ramsey properties of randomly perturbed 3-uniform hypergraphs. For t ≥ 2, write Ket(3) to denote the 3-uniform expanded clique hypergraph obtained from the complete graph Kt by expanding each of the edges of the latter with a new additional vertex. For an even integer t ≥ 4, let M denote the asymmetric maximal density of the pair (Ket(3), Ket/(3)2). We prove that adding a set F of random hyperedges satisfying |F| ≫ n3−1/M to a given n-vertex 3-uniform hypergraph H with non-vanishing edge density asymptotically almost surely results in a perturbed hypergraph enjoying the Ramsey property for Ket(3) and two colours. We conjecture that this result is asymptotically best possible with respect to the size of F whenever t ≥ 6 is even. The key tools of our proof are a new variant of the hypergraph regularity lemma accompanied with a tuple lemma providing appropriate control over joint link graphs. Our variant combines the so called strong and the weak hypergraph regularity lemmata.",

keywords = "Ramsey Theory, Random Hypergraphs, Smoothed Analysis",

author = "Elad Aigner-Horev and Dan Hefetz and Mathias Schacht",

note = "Publisher Copyright: {\textcopyright} Elad Aigner-Horev, Dan Hefetz, and Mathias Schacht.; 27th International Conference on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2024 and the 28th International Conference on Randomization and Computation, RANDOM 2024 ; Conference date: 28-08-2024 Through 30-08-2024",

year = "2024",

month = sep,

doi = "10.4230/LIPIcs.APPROX/RANDOM.2024.59",

language = "אנגלית",

series = "Leibniz International Proceedings in Informatics, LIPIcs",

publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",

editor = "Amit Kumar and Noga Ron-Zewi",

booktitle = "Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2024",

address = "גרמניה",

}