2022/02/12 by Miao Fu, Fei Xue, Fu, Miao +3
Computer Science · Engineering · #05C12 #52B10 #52C07 #52C17 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Metric Geometry (math.MG) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2202.06025
openalex publication_date 2022/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper presents new lower bounds for the lattice covering densities of simplices by studying the Degree-Diameter Problem for abelian Cayley digraphs. In particular, it proves that the density of any lattice covering of a tetrahedron is at least 25/18 and the density of any lattice covering of a four-dimensional simplex is at least 343/264.