Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.16606 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910759069417472 |
|---|---|
| author | Sun, Timothy |
| author_facet | Sun, Timothy |
| contents | We show that for all $n \equiv 0 \pmod{6}$, $n \geq 18$, 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 $n-2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_16606 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Genus embeddings of complete graphs minus a matching Sun, Timothy Combinatorics We show that for all $n \equiv 0 \pmod{6}$, $n \geq 18$, 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 $n-2$. |
| title | Genus embeddings of complete graphs minus a matching |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2412.16606 |