Diana Piguet

AN APPROXIMATE VERSION OF THE TREE PACKING CONJECTURE

We prove that for any pair of constants ɛ > 0 and Δ and for n sufficiently large, every family of trees of orders at most n, maximum degrees at most Δ, and with at most (n2) edges in total packs into

The Approximate Loebl--Komlós--Sós Conjecture III: The Finer Structure of LKS Graphs

{K_{(1 + \varepsilon )n}}

The Approximate Loebl--Komlós--Sós Conjecture IV: Embedding Techniques and the Proof of the Main Result

. This implies asymptotic versions of the Tree Packing Conjecture of Gyárfás from 1976 and a tree packing conjecture of Ringel from 1963 for trees with bounded maximum degree. A novel random tree embedding process combined with the nibble method forms the core of the proof.

The approximate Loebl-Komlos-Sos Conjecture I: The sparse decomposition

Abstract We prove a version of the Loebl-Komlos-Sos Conjecture for large dense graphs. For any q > 0 there exists n 0 ∈ N such that for any n > n 0 holds: If G has median degree at least k, then any tree of order at most k + 1 is a subgraph of G.

A Density Corradi-Hajnal Theorem

This is the third of a series of four papers in which we prove the following relaxation of the Loebl--Komlos--Sos conjecture: For every

Komlós's tiling theorem via graphon covers

\alpha>0

The approximate Loebl-Komlós-Sós conjecture and embedding trees in sparse graphs

there exists a number

Turánnical hypergraphs

k_0