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Excluded-Minor Characterization of Apex-Outerplanar Graphs

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Abstract

The class of outerplanar graphs is minor-closed and can be characterized by two excluded minors: \(K_4\) and \(K_{2,3}\). The class of graphs that contain a vertex whose removal leaves an outerplanar graph is also minor-closed. We provide the complete list of 57 excluded minors for this class.

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Authors and Affiliations

  1. Department of Mathematics, Louisiana State University, Baton Rouge, LA, 70803-4918, USA

    Guoli Ding

  2. Department of Mathematical Sciences, University of Puerto Rico at Mayaguez, Mayagüez, PR, 00681, USA

    Stan Dziobiak

Authors
  1. Guoli Ding
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  2. Stan Dziobiak
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Corresponding author

Correspondence to Stan Dziobiak.

Additional information

G. Ding’s work was supported in part by NSF Grants DMS-1001230 and DMS-1500699.

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Ding, G., Dziobiak, S. Excluded-Minor Characterization of Apex-Outerplanar Graphs. Graphs and Combinatorics 32, 583–627 (2016). https://doi.org/10.1007/s00373-015-1611-9

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  • DOI: https://doi.org/10.1007/s00373-015-1611-9

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