Ramsey numbers for certain k-graphs

Abstract

We are interested here in the Ramsey number r(T,C), where C is a complete /c-uniform hypergraph and T is a "tree-like" A-graph. Upper and lower bounds are found for these numbers which lead, in some cases, to the exact value for r(T, C) and to a generalization of a theorem of Chvatal on Ramsey numbers for graphs. In other cases we show that a determination of the exact values of r( T, C) would be equivalent to obtaining a complete solution to existence question for a certain class of Steiner systems.

Generalizations of a Ramsey‐theoretic result of chvátal

“…Some of this involvés F-goodness [4], [9], or its multicolor version [3], [13], or hypergraphs [5] .…”