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

Abstract

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 $K_{n-1}$.