Balanced 1-Factorisations of 3- and 4-Regular Circulant Graphs
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915039631376384 |
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| author | Mitchell, Jeremy |
| author_facet | Mitchell, Jeremy |
| contents | We investigate 1-factorisations in which the 2-regular graphs that occur as the union of a pair of 1-factors appear an equal number of times across the unions of all pairs of 1-factors in the 1-factorisation. We call such 1-factorisations balanced 1-factorisations (B1Fs) and we present some results on B1Fs of 3- and 4-regular circulant graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_19197 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Balanced 1-Factorisations of 3- and 4-Regular Circulant Graphs Mitchell, Jeremy Combinatorics 05C70 We investigate 1-factorisations in which the 2-regular graphs that occur as the union of a pair of 1-factors appear an equal number of times across the unions of all pairs of 1-factors in the 1-factorisation. We call such 1-factorisations balanced 1-factorisations (B1Fs) and we present some results on B1Fs of 3- and 4-regular circulant graphs. |
| title | Balanced 1-Factorisations of 3- and 4-Regular Circulant Graphs |
| topic | Combinatorics 05C70 |
| url | https://arxiv.org/abs/2411.19197 |