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Minimum Degrees and Codegrees of Ramsey-Minimal 3-Uniform Hypergraphs
Publikationstyp
Journal Article
Date Issued
2016-01-20
Sprache
English
Author(s)
Institut
TORE-URI
Volume
25
Issue
6
Start Page
850
End Page
869
Citation
Combinatorics Probability and Computing 6 (25): 850-869 (2016)
Publisher DOI
Scopus ID
Publisher
Cambridge Univ. Press
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.
DDC Class
510: Mathematik