A long time ago, M. Ajtai, J. Komlós, M. Simonovits, and E. Szemerédi announced a proof (for large $k$) of the Erdős–Sós conjecture that every graph with average degree
more than $k-1$ contains all trees with $k$ edges as subgraphs, but the proof has not yet appeared as of this writing (2022).

What do I mean by "a long time ago"?  Reinhard Diestel, in the notes to Chapter 7 of <i>Graph Theory</i> (5th edition), gives a date of 2009.  But Václav Rozhoň, in <a href="https://arxiv.org/abs/1804.06791">A local approach to the Erdős-Sós conjecture</a>, says that the result was announced in the early 1990's.