Diana Piguet: An approximate version of the Tree Packing Conjecture

A family of graphs packs into a graph G if there exist pairwise edge-disjoint copies of its members in G. We prove a theorem about packing trees into a complete graph. The result implies asymptotic versions of the Tree Packing Conjecture of Gyárfás and the Ringel Conjecture for the class of trees with bounded maximal degree. The core of the proof is a random process controlled by the nibbling method.

This is a joint work with Julia Böttcher, Jan Hladký, and Anusch Taraz.