The Erdős–Sós conjecture for spiders of large size

The Erdős–Sós Conjecture states that if G is a graph with average degree more than k − 1 , then G contains every tree with k edges. A spider is a tree with at most one vertex of degree more than 2. In this paper, we prove that if G is a graph on n vertices with average degree more than k − 1 , then G contains every spider with k edges, where k ≥ n + 5 2 .