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Minimum degrees and codegrees of minimal Ramsey 3-uniform hypergraphs
Publikationstyp
Journal Article
Date Issued
2015-11-12
Sprache
English
Author(s)
Institut
Volume
49
Start Page
23
End Page
30
Citation
Electronic Notes in Discrete Mathematics 49: 23-30 (2015-11)
Publisher DOI
Scopus ID
Publisher
Elsevier Science
A uniform hypergraph H is called k-Ramsey for a hypergraph F, if no matter how one colors the edges of H with k colors, there is always a monochromatic copy of F. We say that H is minimal k-Ramsey for F, if H is k-Ramsey for F but every proper subhypergraph of H is not. Burr, Erdos and Lovasz [S. A. Burr, P. Erdos, and L. Lovász, On graphs of Ramsey type, Ars Combinatoria 1 (1976), no. 1, 167-190] studied various parameters of minimal Ramsey graphs. In this paper we initiate the study of minimum degrees and codegrees of minimal Ramsey 3-uniform hypergraphs. We show that the smallest minimum vertex degree over all minimal k-Ramsey 3-uniform hypergraphs for Kt(3) is exponential in some polynomial in k and t. We also study the smallest possible minimum codegrees over minimal 2-Ramsey 3-uniform hypergraphs.
Subjects
Minimal Ramsey hypergraph
Minimum degree and codegree
DDC Class
510: Mathematik
Funding Organisations
More Funding Information
YP is partially supported by DFG grant PE 2299/1-1.