AUT LibraryAUT
View Item 
  •   Open Research
  • AUT Faculties
  • Faculty of Design and Creative Technologies (Te Ara Auaha)
  • School of Engineering, Computer and Mathematical Sciences - Te Kura Mātai Pūhanga, Rorohiko, Pāngarau
  • View Item
  •   Open Research
  • AUT Faculties
  • Faculty of Design and Creative Technologies (Te Ara Auaha)
  • School of Engineering, Computer and Mathematical Sciences - Te Kura Mātai Pūhanga, Rorohiko, Pāngarau
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

A polychromatic Ramsey theory for ordinals

Huschenbett, M; Liu, J
Thumbnail
View/Open
Polychromatic.pdf (434.1Kb)
Permanent link
http://hdl.handle.net/10292/6737
Metadata
Show full metadata
Abstract
The Ramsey degree of an ordinal α is the least number n such that any colouring of the edges of the complete graph on α using finitely many colours contains an n-chromatic clique of order type α. The Ramsey degree exists for any ordinal α < ω ω . We provide an explicit expression for computing the Ramsey degree given α. We further establish a version of this result for automatic structures. In this version the ordinal and the colouring are presentable by finite automata and the clique is additionally required to be regular. The corresponding automatic Ramsey degree turns out to be greater than the set theoretic Ramsey degree. Finally, we demonstrate that a version for computable structures fails.
Date
2013
Source
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol.8087 LNCS, pp.559 - 570
Item Type
Journal Article
Publisher
Springer Berlin Heidelberg
DOI
10.1007/978-3-642-40313-2_50
Publisher's Version
http://dx.doi.org/10.1007/978-3-642-40313-2_50
Rights Statement
An author may self-archive an author-created version of his/her article on his/her own website and or in his/her institutional repository. He/she may also deposit this version on his/her funder’s or funder’s designated repository at the funder’s request or as a result of a legal obligation, provided it is not made publicly available until 12 months after official publication. He/ she may not use the publisher's PDF version, which is posted on www.springerlink.com, for the purpose of self-archiving or deposit. Furthermore, the author may only post his/her version provided acknowledgement is given to the original source of publication and a link is inserted to the published article on Springer's website. The link must be accompanied by the following text: "The final publication is available at www.springerlink.com”. (Please also see Publisher’s Version and Citation).

Contact Us
  • Admin

Hosted by Tuwhera, an initiative of the Auckland University of Technology Library

 

 

Browse

Open ResearchTitlesAuthorsDateSchool of Engineering, Computer and Mathematical Sciences - Te Kura Mātai Pūhanga, Rorohiko, PāngarauTitlesAuthorsDate

Alternative metrics

 

Statistics

For this itemFor all Open Research

Share

 
Follow @AUT_SC

Contact Us
  • Admin

Hosted by Tuwhera, an initiative of the Auckland University of Technology Library