On tight tree-complete hypergraph Ramsey numbers
Abstract
Chv\'atal showed that for any tree T with k edges the Ramsey number R(T,n)=k(n-1)+1 ("Tree-complete graph Ramsey numbers." Journal of Graph Theory 1.1 (1977): 93-93). For r=3 or 4, we show that, if T is an r-uniform non-trivial tight tree, then the hypergraph Ramsey number R(T,n)=(nr-1). The 3-uniform result comes from observing a construction of Cooper and Mubayi. The main contribution of this paper is the 4-uniform construction, which is inspired by the Cooper-Mubayi 3-uniform construction.
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