Everyone should have a look at Proposition 1.25 (improving the Greenwood and Gleason upper bound on off-diagonal Ramsey numbers by 1, in certain circumstances). We won’t spend much time on this, unless people have questions. It is needed in the proof of Proposition 1.26, so we should at least know the statement and have an idea of its proof.
Joe will present two arguments for a couple of small exact Ramsey numbers (Proposition 1.26 and 1.27).
Everyone should read through propositions 1.26 and 1.27, and the discussion afterwards; I’ll make some further comments on this.
Everyone should think about how a proof for Theorem 1.28 should go; Anthony will tell us about it.
Ryan will present the proof of Theorem 1.29 (a lower bound for the diagonal Ramsey numbers). Everyone should read this proof, too.