What is and is not inside a Cayley graph?
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908578613297152 |
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| author | Knauer, Kolja Gomez, Alvaro Soto |
| author_facet | Knauer, Kolja Gomez, Alvaro Soto |
| contents | In this note we show that there is a cubic graph of girth $5$ that is not a subgraph of any minimal Cayley graph. On the other hand, we show that any Generalized Petersen Graph $G(n,k)$ with $\gcd(n,k)=1$ is an induced subgraph of a minimal Cayley graph. These results give insights into two comments of László Babai in [L. Babai, \emph{Automorphism groups, isomorphism, reconstruction}. Graham, R. L. (ed.) et al., Handbook of combinatorics. Vol. 1-2, 1994]. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_14088 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | What is and is not inside a Cayley graph? Knauer, Kolja Gomez, Alvaro Soto Combinatorics Discrete Mathematics In this note we show that there is a cubic graph of girth $5$ that is not a subgraph of any minimal Cayley graph. On the other hand, we show that any Generalized Petersen Graph $G(n,k)$ with $\gcd(n,k)=1$ is an induced subgraph of a minimal Cayley graph. These results give insights into two comments of László Babai in [L. Babai, \emph{Automorphism groups, isomorphism, reconstruction}. Graham, R. L. (ed.) et al., Handbook of combinatorics. Vol. 1-2, 1994]. |
| title | What is and is not inside a Cayley graph? |
| topic | Combinatorics Discrete Mathematics |
| url | https://arxiv.org/abs/2506.14088 |