English

Loebl-Komlos-Sos Conjecture: dense case

Combinatorics 2017-07-31 v5

Abstract

We prove a version of the Loebl-Komlos-Sos Conjecture for dense graphs. For each q>0 there exists a number n0Nn_0\in \mathbb{N} such that for any n>n_0 and k>qn the following holds: if G be a graph of order n with at least n/2 vertices of degree at least k, then any tree of order k+1 is a subgraph of G.

Keywords

Cite

@article{arxiv.0805.4834,
  title  = {Loebl-Komlos-Sos Conjecture: dense case},
  author = {Jan Hladky and Diana Piguet},
  journal= {arXiv preprint arXiv:0805.4834},
  year   = {2017}
}

Comments

56 pages, 8 figures; substantial changes as suggested by a referee

R2 v1 2026-06-21T10:45:57.063Z