Tree embeddings

We give a general theorem on embedding trees in graphs with certain expanding properties. As an application, we show that for r = ⌊t/18⌋, any graph with average degree greater than t − 1 that does not contain a copy of K_2,r contains every tree with t edges as a subgraph. © 2001 John Wiley & Sons, Inc. J Graph Theory 36: 121–130, 2001