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A note on the Engelking-Karłowicz theorem

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Abstract

We investigate the chromatic number of infinite graphs whose definition is motivated by the theorem of Engelking and Karłowicz (in [?]). In these graphs, the vertices are subsets of an ordinal, and two subsets X and Y are connected iff for some a ∈ X ∩ Y the order-type of a ∩ X is different from that of a ∩ Y.

In addition to the chromatic number x(G) of these graphs we study χ κ (G), the κ-chromatic number, which is the least cardinal µ with a decomposition of the vertices into µ classes none of which contains a κ-complete subgraph.

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Authors and Affiliations

  1. Department of Mathematics, Ben-Gurion University of the Negev, Negev, Israel

    U. Abraham

  2. Department of Mathematics, Carnegie-Mellon University, Pittsburgh, PA, USA

    Y. Yin

Authors
  1. U. Abraham
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  2. Y. Yin
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Correspondence to U. Abraham.

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Abraham, U., Yin, Y. A note on the Engelking-Karłowicz theorem. Acta Math Hung 120, 391–404 (2008). https://doi.org/10.1007/s10474-008-7160-4

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  • DOI: https://doi.org/10.1007/s10474-008-7160-4

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