On the Recognition of Fan-Planar and Maximal Outer-Fan-Planar Graphs

Bekos, Michael A.; Cornelsen, Sabine; Grilli, Luca; Hong, Seok-Hee; Kaufmann, Michael

On the Recognition of Fan-Planar and Maximal Outer-Fan-Planar Graphs

Files

There are no files associated with this item.

Date

2017

Authors

Bekos, Michael A.

Cornelsen, Sabine

Grilli, Luca

Hong, Seok-Hee

Kaufmann, Michael

DOI (citable link)

10.1007/s00453-016-0200-5

Collections

Informatik und Informationswissenschaft

Publication type

Journal article

Publication status

Published

Published in

Algorithmica ; 79 (2017), 2. - pp. 401-427. - ISSN 0178-4617. - eISSN 1432-0541

Abstract

Fan-planar graphs were recently introduced as a generalization of 1-planar graphs. A graph is fan-planar if it can be embedded in the plane, such that each edge that is crossed more than once, is crossed by a bundle of two or more edges incident to a common vertex. A graph is outer-fan-planar if it has a fan-planar embedding in which every vertex is on the outer face. If, in addition, the insertion of an edge destroys its outer-fan-planarity, then it is maximal outer-fan-planar. In this paper, we present a linear-time algorithm to test whether a given graph is maximal outer-fan-planar. The algorithm can also be employed to produce an outer-fan-planar embedding, if one exists. On the negative side, we show that testing fan-planarity of a graph is NP-complete, for the case where the rotation system (i.e., the cyclic order of the edges around each vertex) is given.

Subject (DDC)

004 Computer Science

Keywords

Fan-planar graphs, Beyond planarity, Graph drawing

Cite This

ISO 690

BEKOS, Michael A., Sabine CORNELSEN, Luca GRILLI, Seok-Hee HONG, Michael KAUFMANN, 2017. On the Recognition of Fan-Planar and Maximal Outer-Fan-Planar Graphs. In: Algorithmica. 79(2), pp. 401-427. ISSN 0178-4617. eISSN 1432-0541. Available under: doi: 10.1007/s00453-016-0200-5

BibTex

@article{Bekos2017-10Recog-40478,
  year={2017},
  doi={10.1007/s00453-016-0200-5},
  title={On the Recognition of Fan-Planar and Maximal Outer-Fan-Planar Graphs},
  number={2},
  volume={79},
  issn={0178-4617},
  journal={Algorithmica},
  pages={401--427},
  author={Bekos, Michael A. and Cornelsen, Sabine and Grilli, Luca and Hong, Seok-Hee and Kaufmann, Michael}
}

RDF

<rdf:RDF
    xmlns:dcterms="http://purl.org/dc/terms/"
    xmlns:dc="http://purl.org/dc/elements/1.1/"
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:bibo="http://purl.org/ontology/bibo/"
    xmlns:dspace="http://digital-repositories.org/ontologies/dspace/0.1.0#"
    xmlns:foaf="http://xmlns.com/foaf/0.1/"
    xmlns:void="http://rdfs.org/ns/void#"
    xmlns:xsd="http://www.w3.org/2001/XMLSchema#" > 
  <rdf:Description rdf:about="https://kops.uni-konstanz.de/server/rdf/resource/123456789/40478">
    <dc:contributor>Kaufmann, Michael</dc:contributor>
    <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2017-11-03T10:26:14Z</dcterms:available>
    <dc:contributor>Grilli, Luca</dc:contributor>
    <dcterms:abstract xml:lang="eng">Fan-planar graphs were recently introduced as a generalization of 1-planar graphs. A graph is fan-planar if it can be embedded in the plane, such that each edge that is crossed more than once, is crossed by a bundle of two or more edges incident to a common vertex. A graph is outer-fan-planar if it has a fan-planar embedding in which every vertex is on the outer face. If, in addition, the insertion of an edge destroys its outer-fan-planarity, then it is maximal outer-fan-planar. In this paper, we present a linear-time algorithm to test whether a given graph is maximal outer-fan-planar. The algorithm can also be employed to produce an outer-fan-planar embedding, if one exists. On the negative side, we show that testing fan-planarity of a graph is NP-complete, for the case where the rotation system (i.e., the cyclic order of the edges around each vertex) is given.</dcterms:abstract>
    <dc:creator>Kaufmann, Michael</dc:creator>
    <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2017-11-03T10:26:14Z</dc:date>
    <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/>
    <dcterms:title>On the Recognition of Fan-Planar and Maximal Outer-Fan-Planar Graphs</dcterms:title>
    <dc:contributor>Bekos, Michael A.</dc:contributor>
    <dc:creator>Grilli, Luca</dc:creator>
    <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/36"/>
    <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/36"/>
    <dc:contributor>Cornelsen, Sabine</dc:contributor>
    <dc:creator>Cornelsen, Sabine</dc:creator>
    <dc:language>eng</dc:language>
    <bibo:uri rdf:resource="https://kops.uni-konstanz.de/handle/123456789/40478"/>
    <dc:creator>Bekos, Michael A.</dc:creator>
    <dcterms:issued>2017-10</dcterms:issued>
    <foaf:homepage rdf:resource="http://localhost:8080/"/>
    <dc:creator>Hong, Seok-Hee</dc:creator>
    <dc:contributor>Hong, Seok-Hee</dc:contributor>
  </rdf:Description>
</rdf:RDF>

Bibliography of Konstanz

Yes