A typical decomposition question asks whether the edges of some graph G can
be partitioned into disjoint copies of another graph H. One of the oldest and
best known conjectures in this area, posed by Ringel in 1963, concerns the
decomposition of complete graphs into edge-disjoint copies of a tree. It says
that any tree with n edges packs 2n+1 times into the complete graph
K2n+1. In this paper, we prove this conjecture for large n.Comment: 37 pages, 4 figure