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a/graphtheory posted by smh 6 months ago

Abstract: 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 $$K_{2n + 1}$$. In this paper, we prove this conjecture for large $$n$$