The Erdos-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+52. © 2013 Elsevier B.V. All rights reserved.
Fan, G. (2013). The Erdos-Sós conjecture for spiders of large size. Discrete Mathematics, 313(22), 2513–2517. https://doi.org/10.1016/j.disc.2013.07.021