Dudeney’s Round Table Problem and Neighbour-Balanced Hamilton Decompositions

Dudeney’s round table problem asks for a set of Hamilton cycles in \( K_n \), having the property that each \( 2 \)-path in \( K_n \) lies in exactly one of the cycles. In this paper, we show how to construct a solution of Dudeney’s round table problem for even \( n \) from a semi-antipodal Hamilton decomposition of \( K_{n-1} \).