Minimum Degrees and Codegrees of Ramsey-Minimal 3-Uniform Hypergraphs
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A 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, Erdős 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.
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2013 ◽
Vol Vol. 15 no. 2
(Discrete Algorithms)
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2009 ◽
Vol 18
(5)
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pp. 803-818
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2014 ◽
Vol 672-674
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pp. 1935-1939
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