A solution of Dudeney's round table problem for an even number of people
In 1905 \textit{H. E. Dudeney} [Amusements in Mathematics, Nelson, Lord, 1917; Dover reprint, New York, 1970] asked if \(n\) people could be seated at a round table on \((n-1)\) \((n-2)/2\) consecutive days so that no person would have the same pair of neighbors more than once. Equivalently, this asks for a family of Hamilton cycles in \(K_ n\) so that every 2-path is on exactly one cycle. In this paper the authors provide constructions of these families for all even \(n\). The case when \(n\) is odd is far more difficult and few results are known.
scientific article; zbMATH DE number 165156