A note on packing two copies of a tree into a graph with small maximum degree

Abstract

Let T be a non-star tree of order n and maximum degree Δ. Hong Wang showed that there is a packing σ such that the degree of every vertex v in T⊕σ(T) does not exceed Δ(T)+2. In this note we improve this result in two directions. First, we show that with only one exception, there exists a packing σ such that Δ(T⊕σ(T))≤Δ(T)+1. Moreover, this bound is, in a sense, uniform.