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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…
math.CO2024
On Kainen's conjectures on surface crossing numbers
Timothy Sun
In 1972, Kainen proved a general lower bound on the crossing number of a graph in a closed surface and conjectured that this bound is tight when the graph is either a complete grap…