2023/12/11 by Anton Levonian, Levonian, Anton
Computer Science · Engineering · #Advanced Graph Theory Research #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Metric Geometry (math.MG) #Optimization and Packing Problems
paper · pdf · doi:10.48550/arxiv.2401.10248
openalex publication_date 2023/12/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A translation surface is a surface formed by identifying edges of a collection of polygons in the complex plane that are parallel and of equal length using only translations. We determined that the same circle packing can be realized on varying translation surfaces in a certain stratum. We also determined possible complexities of contacts graphs and provide a bound on this complexity in some low-genus strata. Finally, we established the possibility of certain contacts graphs' complexities in strata with genus greater than 2.