Some Remarks on the Simultaneous Chromatic Number

Combinatorica volume 23, pages89–104(2003)Cite this article

We present several partial results, variants, and consistency results concerning the following (as yet unsolved) conjecture. If X is a graph on the ground set V with \( Chr{\left( X \right)} = {\aleph }_{1} \) then X has an edge coloring F with \( {\aleph }_{1} \) colors such that if V is decomposed into \( {\aleph }_{0} \) parts then there is one in which F assumes all values.

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Affiliations

  1. Rutgers University, Department of Mathematics; Hill Center, Busch Campus, 110 Frelighuysen Road, Piscataway, NJ, 08855-1179, USA

    András Hajnal*

  2. Department of Computer Science, Eötvös University, Budapest, Pázmány P. sétány 1/c, H-1117, Hungary

    Péter Komjáth†

Authors
  1. András Hajnal*
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  2. Péter Komjáth†
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Corresponding author

Correspondence to András Hajnal*.

Additional information

Due to some unfortunate misunderstandings, this paper appeared much later than we expected.

* Research partially supported by NSF grants DMS-9704477 and DMS-0072560.

† Research partially supported by Hungarian National Research Grant T 032455.

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Hajnal*, A., Komjáth†, P. Some Remarks on the Simultaneous Chromatic Number. Combinatorica 23, 89–104 (2003). https://doi.org/10.1007/s00493-003-0015-2

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AMS Subject Classification (2000):

  • 03E35
  • 05C15