Connection Trees and Partition

Question

In our lecture we just had a short excursion into the tree-world.
But the professor mentioned some connection between Ramsey and König's Infinity Lemma (If $T$ is a tree of hight $\omega$ with all levels finite, then $T$ has an infinite branch.).
He wrote that Ramsey implies König, and König implies Ramsey.
Could someone explain me this connection? How do I 'connect' trees and the partition notation?
I hope the question is clear, and someone feels like helping.

Best, Luca!

Answer 1

Your question is essentially answered here.