A strongly non-Ramsey uncountable graph

The Maximum Number of Edges in a Strongly Multiplicative Graph

Cycles Are Strongly Ramsey-Unsaturated

We call a graph H Ramsey-unsaturated if there is an edge in the complement of H such that the Ramsey number r(H) of H does not change upon adding it to H. This notion was introduced by Balister, Lehel and Schelp in [2], where it is shown that cycles (except for C4) are Ramsey-unsaturated, and conjectured that, moreover, one may add any chord without changing the Ramsey number of the cycle Cn, u...

Easton's theorem for Ramsey and strongly Ramsey cardinals

We show that, assuming GCH, if κ is a Ramsey or a strongly Ramsey cardinal and F is a class function on the regular cardinals having a closure point at κ and obeying the constraints of Easton’s theorem, namely, F (α) ≤ F (β) for α ≤ β and α < cf(F (α)), then there is a cofinality preserving forcing extension in which κ remains Ramsey or strongly Ramsey respectively and 2δ = F (δ) for every regu...

Induced Graph Ramsey Theory

We say that a graph F strongly arrows (G, H) and write F ֌ (G, H) if for every edge-coloring of F with colors red and blue a red G or a blue H occurs as an induced subgraph of F . Induced Ramsey numbers are defined by r(G, H) = min{|V (G)| : F ֌ (G, H)}. The value of r(G, H) is finite for all graphs, and good upper bounds on induced Ramsey numbers in general, and for particular families of grap...

Ramsey-type graph coloring and diagonal non-computability

A function is diagonally non-computable (d.n.c.) if it diagonalizes against the universal partial computable function. D.n.c. functions play a central role in algorithmic randomness and reverse mathematics. Flood and Towsner asked for which functions h, the principle stating the existence of an h-bounded d.n.c. function (h-DNR) implies the Ramsey-type König’s lemma (RWKL). In this paper, we pro...