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Cover-Incomparability Graphs of Posets

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A Commentary to this article was published on 18 August 2018

Abstract

Cover-incomparability graphs (C-I graphs, for short) are introduced, whose edge-set is the union of edge-sets of the incomparability and the cover graph of a poset. Posets whose C-I graphs are chordal (resp. distance-hereditary, Ptolemaic) are characterized in terms of forbidden isometric subposets, and a general approach for studying C-I graphs is proposed. Several open problems are also stated.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, FNM, University of Maribor, Koroška 160, 2000, Maribor, Slovenia

    Boštjan Brešar & Matjaž Kovše

  2. Institute of Mathematics, Physics and Mechanics, Ljubljana, Slovenia

    Boštjan Brešar, Sandi Klavžar & Matjaž Kovše

  3. Department of Futures Studies, University of Kerala, Trivandrum, 695034, India

    Manoj Changat & Antony Mathews

  4. Department of Mathematics, University of Ljubljana, Jadranska 19, 1000, Ljubljana, Slovenia

    Sandi Klavžar

  5. University of Maribor, Maribor, Slovenia

    Sandi Klavžar

  6. Chingamparampil, Vazhapally, Changanacherry, 686103, Kerala, India

    Joseph Mathews

Authors
  1. Boštjan Brešar
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  2. Manoj Changat
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  3. Sandi Klavžar
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  4. Matjaž Kovše
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  5. Joseph Mathews
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  6. Antony Mathews
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Correspondence to Sandi Klavžar.

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Brešar, B., Changat, M., Klavžar, S. et al. Cover-Incomparability Graphs of Posets. Order 25, 335–347 (2008). https://doi.org/10.1007/s11083-008-9097-1

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