3 papers
math.CO2025
Orientable triangular embeddings of the complete graphs on 36s vertices from noncyclic current graphs
Avinh Huynh, Timothy Sun
Mark Jungerman's 1975 Ph.D. thesis presents several infinite families of index 2 current graphs that generate triangular embeddings of complete or near-complete graphs. However, th…
math.CO2024
Genus embeddings of complete graphs minus a matching
Timothy Sun
We show that for all , , there is an orientable triangular embedding of the octahedral graph on vertices that can be augmented with handles to p…
math.CO2024
An optimal construction for complete graph embeddings with duals of low connectivity
Timothy Sun
We describe a construction for embeddings of complete graphs where the dual has a cutvertex and the genus is close to the minimum genus of the primal graph. When the number of vert…