Ramsey theory for highly connected monochromatic subgraphs

J. Bergfalk; M. Hrušák; S. Shelah

doi:10.1007/s10474-020-01058-x

Ramsey theory for highly connected monochromatic subgraphs

J. Bergfalk, M. Hrušák^*, S. Shelah

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

An infinite graph is highly connected if the complement of anysubgraph of smaller size is connected. We consider weaker versions of Ramsey’sTheorem asserting that in any coloring of the edges of a complete graph thereexist large highly connected subgraphs all of whose edges are colored by the samecolor.

Original language	English
Pages (from-to)	309-322
Number of pages	14
Journal	Acta Mathematica Hungarica
Volume	163
Issue number	1
DOIs	https://doi.org/10.1007/s10474-020-01058-x
State	Published - Feb 2021

Bibliographical note

Publisher Copyright:
© 2020, Akadémiai Kiadó, Budapest, Hungary.

Keywords

highly connected graph
k-connected graph
Mahlocardinal
Ramsey theory
weakly compact cardinal

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10.1007/s10474-020-01058-x

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Ramsey theory for highly connected monochromatic subgraphs

Abstract

Bibliographical note

Keywords

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