Ringel's tree packing conjecture in quasirandom graphs

Keevash, Peter and Staden, Katherine (2023). Ringel's tree packing conjecture in quasirandom graphs. Journal of the European Mathematical Society (In Press).

DOI: https://doi.org/10.48550/arXiv.2004.09947

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.

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