Exponential Lower Bound for Berge-Ramsey Problems

We give an exponential lower bound for the smallest $$N$$ N such that no matter how we c -color the edges of a complete $$r$$ r -uniform hypergraph on $$N$$ N vertices, we can always find a monochromatic Berge- $$K_n$$ K n .

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Published in	Graphs and combinatorics Vol. 37; no. 4; pp. 1433 - 1435
Main Author	Pálvölgyi, Dömötör
Format	Journal Article
Language	English
Published	Tokyo Springer Japan 01.07.2021 Springer Nature B.V
Subjects	Apexes Combinatorics Engineering Design Graph theory Lower bounds Mathematics Mathematics and Statistics Original Paper Hypergraphs Berge-graph Ramsey theory
Online Access	Get full text
ISSN	0911-0119 1435-5914 1435-5914
DOI	10.1007/s00373-021-02328-3

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Abstract	We give an exponential lower bound for the smallest $$N$$ N such that no matter how we c -color the edges of a complete $$r$$ r -uniform hypergraph on $$N$$ N vertices, we can always find a monochromatic Berge- $$K_n$$ K n .
AbstractList	We give an exponential lower bound for the smallest $$N$$ N such that no matter how we c -color the edges of a complete $$r$$ r -uniform hypergraph on $$N$$ N vertices, we can always find a monochromatic Berge- $$K_n$$ K n . We give an exponential lower bound for the smallest N such that no matter how we c -color the edges of a complete r -uniform hypergraph on N vertices, we can always find a monochromatic Berge- K n . We give an exponential lower bound for the smallest N such that no matter how we c-color the edges of a complete r-uniform hypergraph on N vertices, we can always find a monochromatic Berge-Kn.
Author	Pálvölgyi, Dömötör
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References	Gerbner, Methuku, Omidi, Vizer (CR4) 2020; 34 Conlon, Fox, Rödl (CR2) 2017; 8 Axenovich, Gyárfás (CR1) 2019; 342 Gerbner (CR3) 2020; 27 Gerbner, Palmer (CR5) 2017; 31 Salia, Tompkins, Wang, Zamora (CR6) 2019; 26 D Gerbner (2328_CR4) 2020; 34 D Gerbner (2328_CR3) 2020; 27 D Gerbner (2328_CR5) 2017; 31 N Salia (2328_CR6) 2019; 26 D Conlon (2328_CR2) 2017; 8 M Axenovich (2328_CR1) 2019; 342
References_xml	– volume: 31 start-page: 2314 issue: 4 year: 2017 end-page: 2327 ident: CR5 article-title: Extremal Results for Berge Hypergraphs publication-title: SIAM J. Discrete Math. doi: 10.1137/16M1066191 – volume: 8 start-page: 475 issue: 3 year: 2017 end-page: 485 ident: CR2 article-title: Hedgehogs are not colour blind publication-title: J. Combin. – volume: 26 start-page: P4.40 issue: 4 year: 2019 ident: CR6 article-title: Ramsey numbers of Berge-hypergraphs publication-title: Electro. J. Combin. doi: 10.37236/8892 – volume: 342 start-page: 1245 issue: 5 year: 2019 end-page: 1252 ident: CR1 article-title: A note on Ramsey numbers for Berge-G hypergraphs publication-title: Discrete Math. doi: 10.1016/j.disc.2019.01.011 – volume: 27 start-page: P2.39 issue: 2 year: 2020 ident: CR3 article-title: On Berge-Ramsey problems publication-title: Electro. J. Combin. doi: 10.37236/8775 – volume: 34 start-page: 351 issue: 1 year: 2020 end-page: 369 ident: CR4 article-title: Ramsey problems for Berge hypergraphs publication-title: SIAM J. Discrete Math. doi: 10.1137/18M1225227 – volume: 27 start-page: P2.39 issue: 2 year: 2020 ident: 2328_CR3 publication-title: Electro. J. Combin. doi: 10.37236/8775 – volume: 31 start-page: 2314 issue: 4 year: 2017 ident: 2328_CR5 publication-title: SIAM J. Discrete Math. doi: 10.1137/16M1066191 – volume: 34 start-page: 351 issue: 1 year: 2020 ident: 2328_CR4 publication-title: SIAM J. Discrete Math. doi: 10.1137/18M1225227 – volume: 342 start-page: 1245 issue: 5 year: 2019 ident: 2328_CR1 publication-title: Discrete Math. doi: 10.1016/j.disc.2019.01.011 – volume: 8 start-page: 475 issue: 3 year: 2017 ident: 2328_CR2 publication-title: J. Combin. – volume: 26 start-page: P4.40 issue: 4 year: 2019 ident: 2328_CR6 publication-title: Electro. J. Combin. doi: 10.37236/8892
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Snippet	We give an exponential lower bound for the smallest N such that no matter how we c -color the edges of a complete r -uniform hypergraph on N vertices, we can... We give an exponential lower bound for the smallest $$N$$ N such that no matter how we c -color the edges of a complete $$r$$ r -uniform hypergraph on $$N$$ N... We give an exponential lower bound for the smallest N such that no matter how we c-color the edges of a complete r-uniform hypergraph on N vertices, we can...
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SubjectTerms	Apexes Combinatorics Engineering Design Graph theory Lower bounds Mathematics Mathematics and Statistics Original Paper
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Title	Exponential Lower Bound for Berge-Ramsey Problems
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