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The Erdos-S\'os Conjecture states that every graph with average degree exceeding k-1 contains every tree with k edges as a subgraph. We prove that there are >0 and k₀ N such that the conjecture holds for every tree T with k k₀ edges and every graph G with |V (G) | (1+) |V (T) |.
Reed et al. (Fri,) studied this question.