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.
ISSN: 1469-2163
Journal: Combinatorics, probability & computing 
Institute: Mathematik E-10 
Document Type: Article
Appears in Collections:Publications without fulltext

Show full item record

Page view(s)

Last Week
Last month
checked on Jul 5, 2022

Google ScholarTM


Add Files to Item

Note about this record

Cite this record


Items in TORE are protected by copyright, with all rights reserved, unless otherwise indicated.