Graph Planarity by Replacing Cliques with Paths

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ANGELINI, Patrizio, Peter EADES, Seok-Hee HONG, Karsten KLEIN, Stephen KOBOUROV, Giuseppe LIOTTA, Alfredo NAVARRA, Alessandra TAPPINI, 2020. Graph Planarity by Replacing Cliques with Paths. In: Algorithms. MDPI. 13(8), 194. eISSN 1999-4893. Available under: doi: 10.3390/a13080194

@article{Angelini2020-08-13Graph-51244, title={Graph Planarity by Replacing Cliques with Paths}, year={2020}, doi={10.3390/a13080194}, number={8}, volume={13}, journal={Algorithms}, author={Angelini, Patrizio and Eades, Peter and Hong, Seok-Hee and Klein, Karsten and Kobourov, Stephen and Liotta, Giuseppe and Navarra, Alfredo and Tappini, Alessandra}, note={Article Number: 194} }

<rdf:RDF xmlns:dcterms="" xmlns:dc="" xmlns:rdf="" xmlns:bibo="" xmlns:dspace="" xmlns:foaf="" xmlns:void="" xmlns:xsd="" > <rdf:Description rdf:about=""> <dc:creator>Navarra, Alfredo</dc:creator> <dc:rights>Attribution 4.0 International</dc:rights> <dc:language>eng</dc:language> <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/> <bibo:uri rdf:resource=""/> <dc:contributor>Tappini, Alessandra</dc:contributor> <dspace:hasBitstream rdf:resource=""/> <dc:contributor>Kobourov, Stephen</dc:contributor> <dcterms:isPartOf rdf:resource=""/> <dcterms:hasPart rdf:resource=""/> <dc:creator>Eades, Peter</dc:creator> <dc:creator>Liotta, Giuseppe</dc:creator> <dc:contributor>Eades, Peter</dc:contributor> <dcterms:title>Graph Planarity by Replacing Cliques with Paths</dcterms:title> <dc:creator>Klein, Karsten</dc:creator> <dc:contributor>Klein, Karsten</dc:contributor> <dcterms:abstract xml:lang="eng">This paper introduces and studies the following beyond-planarity problem, which we call h-Clique2Path Planarity. Let G be a simple topological graph whose vertices are partitioned into subsets of size at most h, each inducing a clique. h-Clique2Path Planarity asks whether it is possible to obtain a planar subgraph of G by removing edges from each clique so that the subgraph induced by each subset is a path. We investigate the complexity of this problem in relation to k-planarity. In particular, we prove that h-Clique2Path Planarity is NP-complete even when h=4 and G is a simple 3-plane graph, while it can be solved in linear time when G is a simple 1-plane graph, for any value of h. Our results contribute to the growing fields of hybrid planarity and of graph drawing beyond planarity.</dcterms:abstract> <dc:creator>Angelini, Patrizio</dc:creator> <dspace:isPartOfCollection rdf:resource=""/> <dc:contributor>Navarra, Alfredo</dc:contributor> <dcterms:issued>2020-08-13</dcterms:issued> <dc:contributor>Liotta, Giuseppe</dc:contributor> <dc:creator>Hong, Seok-Hee</dc:creator> <dc:contributor>Hong, Seok-Hee</dc:contributor> <dc:creator>Kobourov, Stephen</dc:creator> <dcterms:available rdf:datatype="">2020-10-07T09:35:26Z</dcterms:available> <dc:date rdf:datatype="">2020-10-07T09:35:26Z</dc:date> <dc:creator>Tappini, Alessandra</dc:creator> <foaf:homepage rdf:resource="http://localhost:8080/jspui"/> <dc:contributor>Angelini, Patrizio</dc:contributor> <dcterms:rights rdf:resource=""/> </rdf:Description> </rdf:RDF>

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