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
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