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Wild edge colourings of graphs

Published online by Cambridge University Press:  12 March 2014

Mirna Džamonja ,
Péter Komjáth  and
Charles Morgan
Mirna Džamonja
Affiliation:
School of Mathematics, University of East Anglia, Norwich, NR4 7TJ, UK, E-mail: M.Dzamonja@uea.ac.uk URL: http://www.mth.uea.ac.uk/people/md.html
Péter Komjáth
Affiliation:
Centre de Recerca Matemàtica, Apartat 50, E-08193 Bellaterra, Spain, E-mail: charles.Morgan@ucl.ac.uk, URL: http://www.ucl.ac.uk/~ucahcjm
Charles Morgan
Affiliation:
Department of Mathematics, University College London, Gower Street, London, WC1E 6BT., UK Department of Computer Science, Eötvös University, Budapest, P.O. Box 120, 1518, Hungary, E-mail: kope@cs.elte.hu, URL: http://www.cs.elte.hu/~kope/
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Abstract

We prove consistent, assuming there is a supercompact cardinal, that there is a singular strong limit cardinal μ, of cofinality ω, such that every μ+-chromatic graph X on μ+ has an edge colouring c of X into μ colours for which every vertex colouring g of X into at most μ many colours has a g-colour class on which c takes every value.

The paper also contains some generalisations of the above statement in which μ+ is replaced by other cardinals > μ.

Keywords

Prikry forcingchromatic numbergraph colourings
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 69 , Issue 1 , March 2004 , pp. 255 - 264
Copyright
Copyright © Association for Symbolic Logic 2004

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References

REFERENCES

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