MORE RAMSEY THEORY FOR HIGHLY CONNECTED MONOCHROMATIC SUBGRAPHS

Michael Hrušák, Saharon Shelah, Jing Zhang

Research output: Contribution to journalArticlepeer-review

Abstract

An infinite graph is said to be highly connected if the induced subgraph on the complement of any set of vertices of smaller size is connected. We continue the study of weaker versions of Ramsey's Theorem on uncountable cardinals asserting that if we color edges of the complete graph we can find a large highly connected monochromatic subgraph. In particular, several questions of Bergfalk, Hrusak and Shelah [5] are answered by showing that assuming the consistency of suitable large cardinals the following are relatively consistent with ZFC:.

Original languageEnglish
JournalCanadian Journal of Mathematics
DOIs
StateAccepted/In press - 2023
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2023 Cambridge University Press. All rights reserved.

Keywords

  • forcing
  • highly connected graph
  • partition relations
  • saturated ideal

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