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Compact Compatible Topologies for Posets and Graphs

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Abstract

A topology on the vertex set of a comparability graph G is said to be compatible (respectively, weakly compatible) with G if each induced subgraph (respectively, each finite induced subgraph) is topologically connected if and only it it is graph-connected; a weakly compatible topology on the vertex set of a graph completely determines the graph structure. We consider here the problem of deciding whether or not a comparability graph has a compact compatible or weakly compatible topology and in the case of graphs with small cycles, hence in the case of trees, we give a characterization.

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Authors and Affiliations

  1. Instituto de Matemáticas, Universidad Nacional Autónoma de México, Ciudad Universitaria, México D.F

    Victor Neumann-Lara

  2. Departamento de Matemáticas, Universidad Autónoma Metropolitana, Unidad Iztapalapa, 09340, México D.F

    Richard G. Wilson

Authors
  1. Victor Neumann-Lara
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  2. Richard G. Wilson
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Neumann-Lara, V., Wilson, R.G. Compact Compatible Topologies for Posets and Graphs. Order 15, 35–50 (1998). https://doi.org/10.1023/A:1006087432310

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  • DOI: https://doi.org/10.1023/A:1006087432310

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