There's a conjecture about graphs, and the conjecture was proven true for a new specific case. So we still don't know whether the conjecture is true in general.

For understanding the conjecture itself, I think the mathematical description is the easier to comprehend than any analogy. See the intro of the Erdős–Hajnal conjecture Wikipedia article[1]. Graphs are pretty intuitive mathematical structures and the description of the conjecture only uses basic graph structures. Although maybe I'm just not clever enough to come up with a suitable analogy.

[1]: https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93Hajnal_conj...