Clemens, DennisDennisClemensPerson, YuryYuryPerson2020-03-252020-03-252016-01-20Combinatorics Probability and Computing 6 (25): 850-869 (2016)http://hdl.handle.net/11420/5490A uniform hypergraph H is called k-Ramsey for a hypergraph F if, no matter how one colours the edges of H with k colours, there is always a monochromatic copy of F. We say that H is k-Ramsey-minimal for F if H is k-Ramsey for F but every proper subhypergraph of H is not. Burr, ErdÅ's and Lovasz studied various parameters of Ramsey-minimal graphs. In this paper we initiate the study of minimum degrees and codegrees of Ramsey-minimal 3-uniform hypergraphs. We show that the smallest minimum vertex degree over all k-Ramsey-minimal 3-uniform hypergraphs for Kt(3) is exponential in some polynomial in k and t. We also study the smallest possible minimum codegree over 2-Ramsey-minimal 3-uniform hypergraphs.en1469-216320166850869Cambridge Univ. PressMathematikJournal Article10.1017/S0963548315000395Other