A local approach to the Erd\H{o}s-S\'os conjecture
Combinatorics
2018-10-30 v2
Abstract
A famous conjecture of Erd\H{o}s and S\'os states that every graph with average degree more than contains all trees with edges as subgraphs. We prove that the Erd\H{o}s-S\'os 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.
Cite
@article{arxiv.1804.06791,
title = {A local approach to the Erd\H{o}s-S\'os conjecture},
author = {Václav Rozhoň},
journal= {arXiv preprint arXiv:1804.06791},
year = {2018}
}