|Publisher DOI:||10.1016/j.endm.2015.06.005||Title:||Minimum degrees and codegrees of minimal Ramsey 3-uniform hypergraphs||Language:||English||Authors:||Clemens, Dennis
|Keywords:||Minimal Ramsey hypergraph; Minimum degree and codegree||Issue Date:||12-Nov-2015||Publisher:||Elsevier Science||Source:||Electronic Notes in Discrete Mathematics 49: 23-30 (2015-11)||Abstract (english):||
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.
|URI:||http://hdl.handle.net/11420/10808||ISSN:||1571-0653||Journal:||Electronic notes in discrete mathematics||Institute:||Mathematik E-10||Document Type:||Article||Funded by:||Deutsche Forschungsgemeinschaft (DFG)||More Funding information:||YP is partially supported by DFG grant PE 2299/1-1.|
|Appears in Collections:||Publications without fulltext|
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