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math.CO2024
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…
math.CO2024
Optimal bounds on the polynomial Schur's theorem
Jaehoon Kim, Hong Liu, Péter Pál Pach
Liu, Pach and Sándor recently characterized all polynomials such that the equation is -Ramsey, that is, any -coloring of contains infinitely ma…
math.CO2024
Extremal density for subdivisions with length or sparsity constraints
Jaehoon Kim, Hong Liu, Yantao Tang +3
Given a graph , a balanced subdivision of is obtained by replacing all edges of with internally disjoint paths of the same length. In this paper, we prove that for any g…