The Approximate Loebl – Komlós – Sós Conjecture and Embedding Trees in Sparse Graphs

  title={The Approximate Loebl – Koml{\'o}s – S{\'o}s Conjecture and Embedding Trees in Sparse Graphs},
  author={Jan Hladk{\'y} and Diana Piguet and Mikl{\'o}s Simonovits and Maya Jakobine Stein and Endre Szemer{\'e}di and Loebl},
Loebl, Komlós and Sós conjectured that every n-vertex graph G with at least n/2 vertices of degree at least k contains each tree T of order k + 1 as a subgraph. We give a sketch of a proof of the approximate version of this conjecture for large values of k. For our proof, we use a structural decomposition which can be seen as an analogue of Szemerédi’s regularity lemma for possibly very sparse graphs. With this tool, each graph can be decomposed into four parts: a set of vertices of huge degree… CONTINUE READING
4 Citations
28 References
Similar Papers


Publications referenced by this paper.
Showing 1-10 of 28 references

The history of degenerate (bipartite) extremal graph problems

  • FS Z. F”uredi, M. Simonovits
  • 2013

Proof of the (n/2− n/2− n/2) conjecture for large n

  • Y. Zhao
  • Electron. J. Combin., 18(1):Paper 27, 61
  • 2011


  • P. E. Haxell, T. Luczak, P. W. Tingley. Ramsey numbers for trees of small maxi degree
  • 22(2):287–320,
  • 2002

Similar Papers

Loading similar papers…