# The tree-packing conjecture for trees of nearly linear maximal degree

## Diana Piguet

*Czech Academy of Sciences*

April 20, 2023, 12:20 in S6

## Abstract

Gyárfás conjectured in 1978 that the edges of the complete graph on n vertices decomposes into any family of trees (T1, T2, ..., Tn), with |V(Ti)|=i. We'll present a solution to this conjecture for families of trees of maximum degree at most c n/(log n), for some fixed c>0.

This is joint work with Peter Allen, Julia Böttcher, Denis Clemens, Jan Hladký, and Anusch Taraz.