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The Zerodivisor Graph of a Qoset

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Abstract

We study colorings of quasiordered sets (qosets) with a least element 0. To any qoset Q with 0 we assign a graph (called a zerodivisor graph) whose vertices are labelled by the elements of Q with two vertices x,y adjacent if the only elements lying below x and y are those lying below 0. We prove that for such graphs, the chromatic number and the clique number coincide.

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Authors and Affiliations

  1. Department of Algebra and Geometry, Palacký University Olomouc, Tr. 17. listopadu 1192/12 , 77146, Olomouc, Czech Republic

    Radomír Halaš

  2. Institute of Discrete Math. and Geometry, Vienna University of Technology, Wiedner Hauptstraße 8–10, 1040, Vienna, Austria

    Helmut Länger

Authors
  1. Radomír Halaš
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  2. Helmut Länger
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Corresponding author

Correspondence to Radomír Halaš.

Additional information

This work is supported by the Research and Development Council of the Czech Government via the project MSM6198959214 and by the project KONTAKT No. 2009/12.

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Halaš, R., Länger, H. The Zerodivisor Graph of a Qoset. Order 27, 343–351 (2010). https://doi.org/10.1007/s11083-009-9120-1

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  • DOI: https://doi.org/10.1007/s11083-009-9120-1

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