Abstract

The Erd?s-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 ? > 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)|. © The Author(s), 2025. Published by Cambridge University Press.