Research demonstrates the Erdős-Sós Conjecture holds for trees with ≥ k edges in graphs, suggesting average degree is critical.
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)| .
No takes yet. Share an insight, caveat, or question.
Reed et al. (2025) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: