3 papers
math.MG2025
An improved lower bound for star-shaped Kakeya sets
Shaoqi Li
In 1971, Cunningham proved that every star-shaped Kakeya set satisfies . In this paper, we show that Cunningham's bound is not optimal and ca…
math.CO2023
Multiple 3-Coloring, an Approach to 4-Coloring of Planar Graphs
Shaoqing Li
A planar graph can be embedded in a piecewise linear manifold, and the lattice on each linear piece can be colored with 3-coloring. If a planar graph can be colored with multiple 3…
math.CO2022
Parameterizing Fullerenes with Vertex Combinations
Shaoqing Li
A fullerene graph can be embedded in a piecewise linear 2-manifold with each non-hexagonal carbon ring corresponding to a cone vertex. Adjacent two or three such vertices can be co…