On the existence of 4-regular matchstick graphs
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2017
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866908816473325568 |
|---|---|
| author | Winkler, Mike Dinkelacker, Peter Vogel, Stefan |
| author_facet | Winkler, Mike Dinkelacker, Peter Vogel, Stefan |
| contents | A matchstick graph is a planar unit-distance graph. We call it \emph{4-regular} if every vertex has degree 4. While examples of 4-regular matchstick graphs with fewer than 63 vertices are known only for $n \in \{52, 54, 57, 60\}$, we prove the existence of such graphs for every integer $n \geq 63$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1705_00293 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | On the existence of 4-regular matchstick graphs Winkler, Mike Dinkelacker, Peter Vogel, Stefan Combinatorics A matchstick graph is a planar unit-distance graph. We call it \emph{4-regular} if every vertex has degree 4. While examples of 4-regular matchstick graphs with fewer than 63 vertices are known only for $n \in \{52, 54, 57, 60\}$, we prove the existence of such graphs for every integer $n \geq 63$. |
| title | On the existence of 4-regular matchstick graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/1705.00293 |