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arXiv · 2512.23802

A Discrete Logarithm Construction for Orthogonal Double Covers of the Complete Graph by Hamiltonian Paths

M. A. Ollis
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Abstract

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.

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M. A. Ollis. 2025-12-29. A Discrete Logarithm Construction for Orthogonal Double Covers of the Complete Graph by Hamiltonian Paths. https://arxiv.org/abs/2512.23802

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