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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2512.23802 |
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| _version_ | 1866912795006599168 |
|---|---|
| author | Ollis, M. A. |
| author_facet | Ollis, M. A. |
| contents | During their investigation of power-sequence terraces, Anderson and Preece briefly mention a construction of a terrace for the cyclic group $\mathbb{Z}_n$ when $n$ is odd and $2n+1$ is prime; it is built using the discrete logarithm modulo $2n+1$. In this short note we see that this terrace gives rise to an orthogonal double cover (ODC) for the complete graph $K_n$ by Hamiltonian paths. This gives infinitely many new values for which such an ODC is known. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_23802 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Discrete Logarithm Construction for Orthogonal Double Covers of the Complete Graph by Hamiltonian Paths Ollis, M. A. Combinatorics 05C70 During their investigation of power-sequence terraces, Anderson and Preece briefly mention a construction of a terrace for the cyclic group $\mathbb{Z}_n$ when $n$ is odd and $2n+1$ is prime; it is built using the discrete logarithm modulo $2n+1$. In this short note we see that this terrace gives rise to an orthogonal double cover (ODC) for the complete graph $K_n$ by Hamiltonian paths. This gives infinitely many new values for which such an ODC is known. |
| title | A Discrete Logarithm Construction for Orthogonal Double Covers of the Complete Graph by Hamiltonian Paths |
| topic | Combinatorics 05C70 |
| url | https://arxiv.org/abs/2512.23802 |