Distinguishing regular graphs from lists
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866929727601639424 |
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| author | Kwaśny, Jakub Stawiski, Marcin |
| author_facet | Kwaśny, Jakub Stawiski, Marcin |
| contents | An edge colouring of a graph is called distinguishing if there is no non-trivial automorphism which preserves it. We prove that every at most countable, finite or infinite, connected regular graph of order at least $7$ admits a distinguishing edge colouring from any set of lists of length $2$. Furthermore, we show that the same holds for connected regular graphs of order $κ$ where $κ$ is a fixed point of the aleph hierarchy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_14728 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Distinguishing regular graphs from lists Kwaśny, Jakub Stawiski, Marcin Combinatorics 05C15, 05C25, 05C63 An edge colouring of a graph is called distinguishing if there is no non-trivial automorphism which preserves it. We prove that every at most countable, finite or infinite, connected regular graph of order at least $7$ admits a distinguishing edge colouring from any set of lists of length $2$. Furthermore, we show that the same holds for connected regular graphs of order $κ$ where $κ$ is a fixed point of the aleph hierarchy. |
| title | Distinguishing regular graphs from lists |
| topic | Combinatorics 05C15, 05C25, 05C63 |
| url | https://arxiv.org/abs/2207.14728 |