A note on the Engelking-Karłowicz theorem

U. Abraham, Y. Yin

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We investigate the chromatic number of infinite graphs whose definition is motivated by the theorem of Engelking and Karłowicz (in [3]). 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 χ(G) of these graphs we study χκ(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.

Original languageEnglish
Pages (from-to)391-404
Number of pages14
JournalActa Mathematica Hungarica
Volume120
Issue number4
DOIs
StatePublished - 1 Sep 2008

Keywords

  • Chromatic number
  • Infinite graphs
  • Singular cardinals

ASJC Scopus subject areas

  • Mathematics (all)

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