The Erdős–Sós conjecture for spiders of large size

The Erdős–Sós Conjecture states that if GG is a graph with average degree more than k−1k−1, then GG contains every tree with kk edges. A spider is a tree with at most one vertex of degree more than 2. In this paper, we prove that if GG is a graph on nn vertices with average degree more than k−1k−1, then GG contains every spider with kk edges, where k≥n+52.