Ramsey numbers are hard to calculate because the complexity of a graph increases dramatically as you add vertices. For a graph with six vertices and two colors, you can run through all the ...

Graph homomorphisms and chromatic numbers are foundational concepts in modern graph theory, with widespread applications that extend from combinatorial optimisation to theoretical computer science.

“It’s kind of amazing that in every huge graph you can find a big one of those. It’s completely not clear.” The first few Ramsey numbers are relatively simple to calculate. Let’s say you want to know ...