Publisher DOI: | 10.1017/S0963548315000395 | Title: | Minimum Degrees and Codegrees of Ramsey-Minimal 3-Uniform Hypergraphs | Language: | English | Authors: | Clemens, Dennis ![]() Person, Yury |
Issue Date: | 20-Jan-2016 | Publisher: | Cambridge Univ. Press | Source: | Combinatorics Probability and Computing 6 (25): 850-869 (2016) | Abstract (english): | 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, 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. |
URI: | http://hdl.handle.net/11420/5490 | ISSN: | 1469-2163 | Journal: | Combinatorics, probability & computing | Institute: | Mathematik E-10 | Document Type: | Article |
Appears in Collections: | Publications without fulltext |
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