A local approach to the Erdős-Sós conjecture
Václav Rozhoň · arXiv (Cornell University) · 2018
A famous conjecture of Erdős and Sós states that every graph with average degree more than $k - 1$ contains all trees with $k$ edges as subgraphs. We prove that the Erdős-Sós conjecture holds approximately, if the size of the embedded tree is linear in the size of the graph, and the maximum degree of the tree is sublinear.