On Mixed Cages of Girth 6
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911420036153344 |
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| author | Araujo-Pardo, Gabriela Mendoza-Cadena, Mirabel |
| author_facet | Araujo-Pardo, Gabriela Mendoza-Cadena, Mirabel |
| contents | A [z,r;g]-mixed cage is a mixed graph of minimum order such that each vertex has z in-arcs, z out-arcs, r edges, and it has girth g. We present an infinite family of mixed graphs with girth 6. This construction also provides an upper bound on the minimum order of mixed cages of girth 6. Additionally,we introduce a lower bound on the minimum order for any mixed cage. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_14768 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Mixed Cages of Girth 6 Araujo-Pardo, Gabriela Mendoza-Cadena, Mirabel Combinatorics A [z,r;g]-mixed cage is a mixed graph of minimum order such that each vertex has z in-arcs, z out-arcs, r edges, and it has girth g. We present an infinite family of mixed graphs with girth 6. This construction also provides an upper bound on the minimum order of mixed cages of girth 6. Additionally,we introduce a lower bound on the minimum order for any mixed cage. |
| title | On Mixed Cages of Girth 6 |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2401.14768 |