Ringel's tree packing conjecture in quasirandom graphs

TL;DR

This paper proves that quasirandom graphs can be decomposed into multiple copies of any fixed tree, confirming Ringel's conjecture for complete graphs and advancing understanding of graph decompositions.

Contribution

It establishes that quasirandom graphs can be decomposed into copies of any fixed tree, confirming Ringel's conjecture in the case of complete graphs.

Findings

Quasirandom graphs can be decomposed into copies of any fixed tree.

Confirmed Ringel's conjecture for complete graphs.

Provides a decomposition method for quasirandom graphs.

Abstract

We prove that any quasirandom graph with $n$ vertices and $rn$ edges can be decomposed into $n$ copies of any fixed tree with $r$ edges. The case of decomposing a complete graph establishes a conjecture of Ringel from 1963.