58 citations · 220 across the 56 of their papers we have counts for
8 papers · 1 filter
Ramsey numbers of cycles versus general graphs
John Haslegrave, Joseph Hyde, Jaehoon Kim +1
The Ramsey number is the minimum number such that any -vertex graph either contains a copy of or its complement contains . Burr in 1981 proved a pleasingly g…
New lower bounds on kissing numbers and spherical codes in high dimensions
Irene Gil Fernández, Jaehoon Kim, Hong Liu +1
Let the kissing number be the maximum number of non-overlapping unit balls in that can touch a given unit ball. Determining or estimating the number has…
Fractional Helly theorem for Cartesian products of convex sets
Debsoumya Chakraborti, Jaehoon Kim, Jinha Kim +2
Helly's theorem and its variants show that for a family of convex sets in Euclidean space, local intersection patterns influence global intersection patterns. A classical result of…
Well-mixing vertices and almost expanders
Debsoumya Chakraborti, Jaehoon Kim, Jinha Kim +2
We study regular graphs in which the random walks starting from a positive fraction of vertices have small mixing time. We prove that any such graph is virtually an expander and ha…
Shape of the asymptotic maximum sum-free sets in integer lattice grids
Hong Liu, Guanghui Wang, Laurence Wilkes +1
We determine the shape of all sum-free sets in of size close to the maximum , solving a problem of Elsholtz and Rackham. We show that all such…
Crux and long cycles in graphs
John Haslegrave, Jie Hu, Jaehoon Kim +3
We introduce a notion of the \emph{crux} of a graph , measuring the order of a smallest dense subgraph in . This simple-looking notion leads to some generalisations of known…
Nested cycles with no geometric crossings
Irene Gil Fernández, Jaehoon Kim, Younjin Kim +1
In 1975, Erdős asked the following question: what is the smallest function for which all graphs with vertices and edges contain two edge-disjoint cycles and…
Geometric constructions for Ramsey-Turán theory
Hong Liu, Christian Reiher, Maryam Sharifzadeh +1
Combining two classical notions in extremal combinatorics, the study of Ramsey-Turán theory seeks to determine, for integers and , the number $\mathsf{RT}_p(n,K_…