11 papers · 1 filter
On a weaker notion of cross -intersecting families
Jiangdong Ai, Ming Chen, Seokbeom Kim +1
We prove that if two families and satisfy $\sum_{1 \leq i, j \leq \ell} \lvert F_i \cap F_j' \rvert…
Anticoncentration of random spanning trees in almost regular graphs
Hyunwoo Lee
The celebrated formula of Otter \emph{[Ann. of Math. (2) 49 (1948), 583--599]} asserts that the complete graph contains exponentially many non-isomorphic spanning trees. In this pa…
Product representations of polynomials over finite fields
Hyunwoo Lee, Chi Hoi Yip, Semin Yoo
Erdős, Sárközy, and Sós studied the asymptotics of the maximum size of a subset of such that it does not contain distinct elements whose product is a perfec…
On Sidorenko exponents of hypergraphs
Hyunwoo Lee
For an -graph , define Sidorenko exponent as where de…
Spanning clique subdivisions in pseudorandom graphs
Hyunwoo Lee, Matías Pavez-Signé, Teo Petrov
In this paper, we study the appearance of a spanning subdivision of a clique in graphs satisfying certain pseudorandom conditions. Specifically, we show the following three results…
On high discrepancy -factorizations of complete graphs
Jiangdong Ai, Fankang He, Seonghyuk Im +1
We proved that for every sufficiently large , the complete graph with an arbitrary edge signing admits a high discrepancy -factor decom…
Reconstructing hypergraph matching polynomials
Donggyu Kim, Hyunwoo Lee
By utilizing the recently developed hypergraph analogue of Godsil's identity by the second author, we prove that for all , one can reconstruct the matching polynom…
A quantitative improvement on the hypergraph Balog-Szemerédi-Gowers theorem
Hyunwoo Lee
In this note, we obtain a quantitative improvement on the hypergraph variant of the Balog-Szemerédi-Gowers theorem due to Sudakov, Szemerédi, and Vu [Duke Math. J.129.1 (2005): 129…
Random matchings in linear hypergraphs
Hyunwoo Lee
For a given hypergraph and a vertex , consider a random matching chosen uniformly from the set of all matchings in In Kahn conjectured that if i…
Dirac's theorem for linear hypergraphs
Seonghyuk Im, Hyunwoo Lee
Dirac's theorem states that any -vertex graph with even integer satisfying contains a perfect matching. We generalize this to -uniform linear hypergra…
Towards a high-dimensional Dirac's theorem
Hyunwoo Lee
Dirac's theorem determines the sharp minimum degree threshold for graphs to contain perfect matchings and Hamiltonian cycles. There have been various attempts to generalize this th…