Packing two copies of a tree into its fourth power

摘要

It is well known that if a tree T of order n is not a star, then there exists an edge-disjoint placement of two copies of this tree into the complete graph K_n. We improve this result by proving that actually two copies of T can be edge-disjointly packed in a much smaller graph, namely in T~4, the 4th power of T.