English

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 k1k - 1 contains all trees with kk 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.

Keywords

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}
}