The Cycle Counts of Graphs
Fuente:
arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | |
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| _version_ | 1866909929920528384 |
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| author | McCulloch, Ryan McKay, Brendan D. Salahshoori, Alireza Zaslavsky, Thomas |
| author_facet | McCulloch, Ryan McKay, Brendan D. Salahshoori, Alireza Zaslavsky, Thomas |
| contents | We prove that an inseparable graph can have any positive number of cycles with the six exceptions 2, 4, 5, 8, 9, 16, and that an inseparable cubic graph has the additional exceptions 1 and 13. The exceptions for simple inseparable cubic graphs are unknown. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_02260 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Cycle Counts of Graphs McCulloch, Ryan McKay, Brendan D. Salahshoori, Alireza Zaslavsky, Thomas Combinatorics 05C38 We prove that an inseparable graph can have any positive number of cycles with the six exceptions 2, 4, 5, 8, 9, 16, and that an inseparable cubic graph has the additional exceptions 1 and 13. The exceptions for simple inseparable cubic graphs are unknown. |
| title | The Cycle Counts of Graphs |
| topic | Combinatorics 05C38 |
| url | https://arxiv.org/abs/2507.02260 |