Abstract

The Erdős-Sós 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 δ > 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 + δ)|V(T)|. © The Author(s), 2025. Published by Cambridge University Press.