Generalized Ramsey theorems for r-uniform hypergraphs

We show that several known Ramsey number inequalities can be extended to the setting of r-uniform hypergraphs. In particular, we extend Burr’s results on tree-star Ramsey numbers, providing exact evaluations for certain hypergraph Ramsey numbers. Then we turn our attention to proving a general multicolor hypergraph Ramsey number inequality from which generalizations of results due to Chvátal and Harary and Robertson can be obtained. Finally, we consider ways in which one may generalize a more recent multicolor Ramsey number inequality due to Xiaodong, Zheng, Exoo, and Radziszowski. M. BUDDEN ET AL. /AUSTRALAS. J. COMBIN. 63 (1) (2015), 142–152 143