Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-22T16:42:23.956Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [email protected] 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: [email protected], 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: [email protected], URL: http://www.cs.elte.hu/~kope/
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Džamonja, M. and Shelah, S., Universal graphs at the successor of a singular cardinal, this Journal, vol. 68 (2003), no. 2, pp. 366–388.Google Scholar
[2]Fodor, G., Proof of a conjecture of P. Erdős, Acta Scientiarum Mathematicarum, Universitatis Szegediensis, vol. 14 (1952), pp. 219–227.Google Scholar
[3]Hajnal, A. and Hamburger, P., Set theory, London Mathematical Society Student Texts, vol. 48, Cambridge University Press, 1999.CrossRefGoogle Scholar
[4]Hajnal, A. and Komjáth, P., Some remarks on the simultaneous chromatic number, Paul Erdős and his mathematics (Halász, G., Lovász, L., Simonovits, M., and Sós, V. T., editors), Bolyai Society Mathematical Studies, vol. 10.Google Scholar
[5]Laver, R., Making the supercompactness of κ indestructible under κ-directed closed forcing, Israel Journal of Mathematics, vol. 29 (1978), no. 4, pp. 385–388.CrossRefGoogle Scholar
[6]Shelah, S., Cardinal arithmetic, Oxford University Press, 1994.CrossRefGoogle Scholar
[7]Todorčević, S., Coloring pairs of countable ordinals, Acta Mathematica, vol. 159 (1987), pp. 261–294.Google Scholar