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Coloring of universal graphs

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Abstract

LetG be a graph andr a cardinal number. Extending the theorem of J. Folkman we show that if eitherr or clG are finite then there existsH with clH = clG andH → (G) 1r . Answering a question of A. Hajnal we show that countably universal graphU 3 satisfiesU 3 → (U3) 1r for every finiter.

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Authors and Affiliations

  1. Department of Mathematics, Eötvös University, H-1088, Budapest, Hungary

    Peter Komjáth

  2. Department of Mathematics, FJFI ČVUT, HUSOVA1, Praha 1, Czechoslovakia

    Vojtèch Rödl

  3. AT&T Bell Laboratories, 07974, Murray Hill, NJ, USA

    Vojtèch Rödl

Authors
  1. Peter Komjáth
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  2. Vojtèch Rödl
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Komjáth, P., Rödl, V. Coloring of universal graphs. Graphs and Combinatorics 2, 55–60 (1986). https://doi.org/10.1007/BF01788077

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  • DOI: https://doi.org/10.1007/BF01788077

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