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Properly Edge-Coloured Subgraphs in Colourings of Bounded Degree
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2011 (English)In: Graphs and Combinatorics, ISSN 0911-0119, E-ISSN 1435-5914, Vol. 27, no 2, 243-249 p.Article in journal (Refereed) Published
Abstract [en]

The smallest n such that every colouring of the edges of K (n) must contain a monochromatic star K (1,s+1) or a properly edge-coloured K (t) is denoted by f (s, t). Its existence is guaranteed by the ErdAs-Rado Canonical Ramsey theorem and its value for large t was discussed by Alon, Jiang, Miller and Pritikin (Random Struct. Algorithms 23:409-433, 2003). In this note we primarily consider small values of t. We give the exact value of f (s, 3) for all s a parts per thousand yen 1 and the exact value of f (2, 4), as well as reducing the known upper bounds for f (s, 4) and f (s, t) in general.

Place, publisher, year, edition, pages
Tokyo: Springer-Verlag Tokyo Inc., 2011. Vol. 27, no 2, 243-249 p.
Keyword [en]
properly edge-coloured, rainbow, canonical ramsey theorem, constrained ramsey numbers, graphs
National Category
Discrete Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-52108DOI: 10.1007/S00373-010-0970-5ISI: 000287210400010OAI: oai:DiVA.org:umu-52108DiVA: diva2:496884
Available from: 2012-02-10 Created: 2012-02-10 Last updated: 2017-12-07Bibliographically approved

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Markström, Klas

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