Packing trees into n-chromatic graphs

Abstract

Let Ti denote a tree with i edges. The author’s tree packing conjecture [3] states that Kn has an edge disjoint decomposition into any given sequence T1, T2, . . . Tn−1 of trees. Gerbner, Keszegh and Palmer extended the conjecture by replacing Kn with an arbitrary n-chromatic graph (Conjecture 2 in [1]). Here we show that the extended conjecture follows from the original one. We need the following, perhaps folklore result (Theorem 1 in [4]) and for convenience we include its simple proof.