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Upper Maximal Graphs of Posets

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Abstract

We introduce and study a class of simple graphs, the upper-maximal graphs (UM-graphs), associated to finite posets. The vertices of the UM-graph of a given poset P are the elements of P, and edges are formed by those vertices x and y whenever any maximal element of P that is greater than x is also greater than y or vise versa. We show that the class of UM-graphs constitutes a subclass of comparability graphs. We further provide a characterization of chordal UM-graphs, and compare UM-graphs with known bound graphs of posets.

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Authors and Affiliations

  1. Department of Mathematics, Suleyman Demirel University, Isparta, 32260, Turkey

    Yusuf Civan

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  1. Yusuf Civan
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Correspondence to Yusuf Civan.

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The author is supported by TÜBA through Young Scientist Award Program (TÜBA-GEBİP 2008/08).

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Civan, Y. Upper Maximal Graphs of Posets. Order 30, 677–688 (2013). https://doi.org/10.1007/s11083-012-9270-4

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  • DOI: https://doi.org/10.1007/s11083-012-9270-4

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Mathematics Subject Classification (2010)