5 papers
New lower bound on ball packing density in high-dimensional hyperbolic spaces
Irene Gil Fernández, Jaehoon Kim, Hong Liu +1
We present a new lower bound on the Bowen-Radin maximal density of radius-R ball packings in the m-dimensional hyperbolic space, improving on the basic covering bound by factor Ω(m…
Disjoint isomorphic balanced clique subdivisions
Irene Gil Fernández, Joseph Hyde, Hong Liu +2
A thoroughly studied problem in Extremal Graph Theory is to find the best possible density condition in a host graph for guaranteeing the presence of a particular subgraph …
How to build a pillar: a proof of Thomassen's conjecture
Irene Gil Fernández, Hong Liu
Carsten Thomassen in 1989 conjectured that if a graph has minimum degree more than the number of atoms in the universe (), then it contains a pillar, which is…
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…
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…