On the existence of 4-regular matchstick graphs
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2017
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866908816473325568 |
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| 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 |