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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.10159 |
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| _version_ | 1866913645569507328 |
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| author | Forbes, Anthony Rutherford, Carrie |
| author_facet | Forbes, Anthony Rutherford, Carrie |
| contents | A regular-graph design is a block design for which a pair $\{a,b\}$ of distinct points occurs in $λ+1$ or $λ$ blocks depending on whether $\{a,b\}$ is or is not an edge of a given $δ$-regular graph. Our paper describes a specific construction for regular-graph designs with $λ= 1$ and block size $δ+ 1$. We show that for $δ\in \{2,3\}$, certain necessary conditions for the existence of such a design with $n$ points are sufficient, with two exceptions in each case and two possible exceptions when $δ= 3$. We also construct designs of orders 105 and 117 for connected 4-regular graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_10159 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A construction for regular-graph designs Forbes, Anthony Rutherford, Carrie Combinatorics 05B25 A regular-graph design is a block design for which a pair $\{a,b\}$ of distinct points occurs in $λ+1$ or $λ$ blocks depending on whether $\{a,b\}$ is or is not an edge of a given $δ$-regular graph. Our paper describes a specific construction for regular-graph designs with $λ= 1$ and block size $δ+ 1$. We show that for $δ\in \{2,3\}$, certain necessary conditions for the existence of such a design with $n$ points are sufficient, with two exceptions in each case and two possible exceptions when $δ= 3$. We also construct designs of orders 105 and 117 for connected 4-regular graphs. |
| title | A construction for regular-graph designs |
| topic | Combinatorics 05B25 |
| url | https://arxiv.org/abs/2409.10159 |