Transversals via regularity

Y Cheng, K Staden - arXiv preprint arXiv:2306.03595, 2023 - arxiv.org
Given graphs $ G_1,\ldots, G_s $ all on the same vertex set and a graph $ H $ with $ e
(H)\leq s $, a copy of $ H $ is transversal or rainbow if it contains at most one edge from each …

Robust Hamiltonicity

F Joos, R Lang, N Sanhueza-Matamala - arXiv preprint arXiv:2312.15262, 2023 - arxiv.org
We study conditions under which a given hypergraph is randomly robust Hamiltonian, which
means that a random sparsification of the host graph contains a Hamilton cycle with high …

Factors and loose Hamilton cycles in sparse pseudo‐random hypergraphs

H Han, J Han, P Morris - Random Structures & Algorithms, 2022 - Wiley Online Library
We investigate the emergence of subgraphs in sparse pseudo‐random k‐uniform
hypergraphs, using the following comparatively weak notion of pseudo‐randomness. A k …

Ramsey--Dirac theory for bounded degree hypertrees

J Han, S Im, J Kim, D Yang - arXiv preprint arXiv:2411.17996, 2024 - arxiv.org
Ramsey--Tur\'an theory considers Tur\'an type questions in Ramsey-context, asking for the
existence of a small subgraph in a graph $ G $ where the complement $\overline {G} $ lacks …

Localised codegree conditions for tight Hamilton cycles in 3-uniform hypergraphs

P Araújo, S Piga, M Schacht - arXiv preprint arXiv:2005.11942, 2020 - arxiv.org
We study sufficient conditions for the existence of Hamilton cycles in uniformly dense $3 $-
uniform hypergraphs. Problems of this type were first considered by Lenz, Mubayi, and …

Tight Hamilton cycles in cherry-quasirandom 3-uniform hypergraphs

E Aigner-Horev, G Levy - Combinatorics, Probability and Computing, 2021 - cambridge.org
We employ the absorbing-path method in order to prove two results regarding the
emergence of tight Hamilton cycles in the so-called two-path or cherry-quasirandom 3 …

Non-linear Hamilton cycles in linear quasi-random hypergraphs

J Han, X Shu, G Wang - Proceedings of the 2021 ACM-SIAM Symposium on …, 2021 - SIAM
A k-graph H is called (p, μ)-dense if for all not necessarily disjoint sets A 1,…, Ak⊆ V (H) we
have e (A 1,…, Ak)≥ p| A 1| ⃛| Ak|–μ| V (H)| k. This is believed to be the weakest form of …

Hamiltonicity in Cherry-quasirandom 3-graphs

L Gan, J Han - European Journal of Combinatorics, 2022 - Elsevier
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Localized codegree conditions for tight Hamilton cycles in 3-uniform hypergraphs

P Araújo, S Piga, M Schacht - SIAM Journal on Discrete Mathematics, 2022 - SIAM
We study sufficient conditions for the existence of Hamilton cycles in uniformly dense 3-
uniform hypergraphs. Problems of this type were first considered by Lenz, Mubayi, and …

Clique factors in pseudorandom graphs

P Morris - Journal of the European Mathematical Society, 2023 - ems.press
An n-vertex graph is said to to be. p; ˇ/-bijumbled if for any vertex sets A; B Â VG/, we have
eA; B/D pjAjjBj ˇpjAjjBj: We prove that for any r 2 N 3 and c> 0 there exists an"> 0 such that …