Chapter "Colorings of graphs and Ramsey's theorem" from [A Course in Combinatorics].
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Detailed Description
Chapter "Colorings of graphs and Ramsey's theorem" from [A Course in Combinatorics].
Brook's theorem
Greedy colouring

See "Greedy colouring" in ComputerAlgebra/Hypergraphs/Lisp/plans/Colouring.hpp.

Greedy graph colouring will always find a colouring using at most d + 1 many colours, where d is the maxima degree.

Likely it does not automatically yield a dcolouring if no component is an odd cycle or the graph does not contain a (d+1)clique  example?

Can this be repaired?

Or with other algorithms? Is it possible at all?
On the automorphism group of Ramsey hypergraphs
Finding Ramsey numbers via SAT

Some experimentation has been started in this area at Experimentation/Investigations/RamseyTheory/plans/RamseyProblems.hpp .
On the automorphism group of Ramsey clausesets
Tournaments and transitive tournaments

See [Ramsey numbers for tournaments] by Y.Mannoussakis and Z.Tuza, and originally [A problem on tournaments] by P.Erdos and L.Moser, for work on treating tournaments and transitive subtournaments as a Ramseytype problem, as well as other Ramseytype problems of directed graphs.
The Lovasz local lemma
Definition in file Chapter03.hpp.