All Questions

A classic result of Sierpiński shows that $2^{\aleph_0}\nrightarrow [\aleph_1]^2_2$, that is, there is a coloring of pairs of real numbers using two colors such that both colors appear on any ...

Frank Plumpton Ramsey, best known for giving his name to Ramsey Theory, presented the following theorem in On a Problem of Formal Logic, that was submitted in 1928 and published posthumously. Let $\...

A two-coloring is done over the (infinite) set all incompressible strings (in some chosen alphabet); such that, an edge between two strings is blue if and only if, the strings are of equal lengths and ...

Question: Find/compute relations between the classical Ramsey numbers and their variations (described below) -- exact or asymptotic. A graph is a set $\ X\ $ together with a (coloring) function $\ c:\...