A Simple Visual Proof of a Powerful Idea in Graph Theory - Facts So Romantic
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Ramsey’s theorem predicts a surprising (and useful) consistency in the organization of graphs. Here’s a simple visual proof of how it works.Image by Lucy Reading-Ikkanda/Quanta Magazine; Source: Jonathan Jedwab, Simon Fraser UniversityReprinted with permission from Quanta AbstractionsA recent advance in geometry makes heavy use of Ramsey’s theorem, an important idea in another field—graph theory. Ramsey’s theorem states that in any graph where all points are connected by either red lines or blue lines, you’re guaranteed to have a large subset of the graph that is completely uniform—that is, either all red or all blue. Equivalently, you can go the other way: Pick how big you want your uniform subset to be. Ramsey’s theorem states that somewhere out there there’s a graph in which a subset of (...)