Proof of a Packing Conjecture of Bollobás

Abstract

Béla Bollobás [1] conjectured the following. For any positive integer Δ and real 0 < c < ½ there exists an n 0 with the following properties. If n ≥ n 0 , T is a tree of order n and maximum degree Δ, and G is a graph of order n and maximum degree not exceeding cn , then there is a packing of T and G . Here we prove this conjecture. Auxiliary Theorem 2.1 is of independent interest.