Vopenka's Principle is a large cardinal axiom that has several equivalent formulations. Arguably the simplest is the statement

For every proper class of graphs there exists a non-identity homomorphism between two graphs in that class.

Papers on Vopenka's Principle (VP) go back to 1965. In 1988, Adamek, Rosicky, and Trnkova introduced the Weak Vopenka Principle (WVP), proved that VP implies WVP, and asked if WVP implied VP. This was finally answered in 2019 by Trevor Wilson (published in Advances). From the abstract:

Vopenka’s Principle says that the category of graphs has no large discrete full subcategory, or equivalently that the category of ordinals cannot be fully embedded into it. Weak Vopenka's Principle is the dual statement, which says that the opposite category of ordinals cannot be fully embedded into the category of graphs. It was introduced in 1988 by Adamek, Rosicky, and Trnkova, who showed that it follows from Vopenka’s Principle and asked whether the two statements are equivalent. We show that they are not.