2024/12/21 by Timothy Sun, Sun, Timothy
Computer Science · Mathematics · #Cooperative Communication and Network Coding #Advanced Graph Theory Research #Limits and Structures in Graph Theory
paper · pdf · doi:10.48550/arxiv.2412.16606
We show that for all n ≡ 0 \pmod6, n ≥ 18, there is an orientable triangular embedding of the octahedral graph on n vertices that can be augmented with handles to produce a genus embedding of the complete graph of the same order. For these values of n, the intermediate embeddings of the construction also determine some surface crossing numbers of the complete graph on n vertices and the genus of all graphs on n vertices and minimum degree n-2.