Partitioning the edges of the complete graphs into trees or cycles

by the Tuesday Afternoon Club

The k(2k-1) edges of the complete 2k-graph can be partitioned into k subspanning trees. We demonstrate the construction for 2k=8:

the three remaining trees are obtained by successive rotations over π/4.

The k(2k+1) edges of the complete (2k+1)-graph can be partitioned into k subspanning cycles. We demonstrate the construction for 2k+1=9:

the three remaining cycles are obtained by successive rotations over π/4.