Some Cyclic Solutions to the Three Table Oberwolfach Problem

  • M. A. Ollis


We use graceful labellings of paths to give a new way of constructing terraces for cyclic groups. These terraces are then used to find cyclic solutions to the three table Oberwolfach problem, ${\rm OP}(r,r,s)$, where two of the tables have equal size. In particular we show that, for every odd $r \geq 3$ and even $r$ with $4 \leq r \leq 16$, there is a number $N_r$ such that there is a cyclic solution to ${\rm OP}(r,r,s)$ whenever $s \geq N_r$. The terraces we are able to construct also prove a conjecture of Anderson: For all $m \geq 3$, there is a terrace of ${\Bbb Z}_{2m}$ which begins $0, 2k, k, \ldots$ for some $k$.

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