Open Collections

Description

We prove that given any sequence of $n$ bounded degree trees so that the $j$th tree has $j$ vertices, the complete graph on $n$ vertices has a decomposition into these trees, if $n$ is large enough. This shows that the tree packing conjecture of Gyarfas and Lehel from 1976 holds for all bounded degree trees. An important ingredient is a new tool for constructing approximate decompositions of dense quasirandom graphs into bounded degree graphs (which can be viewed as an extension of the classical blow-up lemma of Komlos, Sarkozy and Szemeredi to the setting of approximate decompositions). (Joint work Felix Joos, Jaehoon Kim, Deryk Osthus and Mykhaylo Tyomkyn)