Morphing Contact Representations of Graphs

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ANGELINI, Patrizio, Steven CHAPLICK, Sabine CORNELSEN, Giordano DA LOZZO, Vincenzo ROSELLI, 2019. Morphing Contact Representations of Graphs. 35th International Symposium on Computational Geometry (SoCG 2019). Portland, United States, Jun 18, 2019 - Jun 21, 2019. In: BAREQUET, Gill, ed., Yusu WANG, ed.. 35th International Symposium on Computational Geometry (SoCG 2019). Wadern:Schloss Dagstuhl - Leibniz-Zentrum für Informatik. eISSN 1868-8969. Available under: doi: 10.4230/LIPIcs.SoCG.2019.10

@inproceedings{Angelini2019Morph-45596, title={Morphing Contact Representations of Graphs}, year={2019}, doi={10.4230/LIPIcs.SoCG.2019.10}, number={129}, address={Wadern}, publisher={Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, series={LIPIcs : Leibniz International Proceedings in Informatics}, booktitle={35th International Symposium on Computational Geometry (SoCG 2019)}, editor={Barequet, Gill and Wang, Yusu}, author={Angelini, Patrizio and Chaplick, Steven and Cornelsen, Sabine and Da Lozzo, Giordano and Roselli, Vincenzo} }

<rdf:RDF xmlns:dcterms="" xmlns:dc="" xmlns:rdf="" xmlns:bibo="" xmlns:dspace="" xmlns:foaf="" xmlns:void="" xmlns:xsd="" > <rdf:Description rdf:about=""> <dc:contributor>Chaplick, Steven</dc:contributor> <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/> <dc:creator>Da Lozzo, Giordano</dc:creator> <dcterms:rights rdf:resource=""/> <dc:contributor>Da Lozzo, Giordano</dc:contributor> <dcterms:available rdf:datatype="">2019-04-05T12:30:58Z</dcterms:available> <dc:date rdf:datatype="">2019-04-05T12:30:58Z</dc:date> <dcterms:isPartOf rdf:resource=""/> <dc:contributor>Angelini, Patrizio</dc:contributor> <dc:creator>Roselli, Vincenzo</dc:creator> <dc:contributor>Cornelsen, Sabine</dc:contributor> <dc:creator>Cornelsen, Sabine</dc:creator> <dc:language>eng</dc:language> <dcterms:title>Morphing Contact Representations of Graphs</dcterms:title> <dc:rights>Attribution 4.0 International</dc:rights> <dspace:hasBitstream rdf:resource=""/> <dcterms:issued>2019</dcterms:issued> <dspace:isPartOfCollection rdf:resource=""/> <bibo:uri rdf:resource=""/> <dcterms:hasPart rdf:resource=""/> <foaf:homepage rdf:resource="http://localhost:8080/jspui"/> <dc:creator>Chaplick, Steven</dc:creator> <dc:contributor>Roselli, Vincenzo</dc:contributor> <dcterms:abstract xml:lang="eng">We consider the problem of morphing between contact representations of a plane graph. In a contact representation of a plane graph, vertices are realized by internally disjoint elements from a family of connected geometric objects. Two such elements touch if and only if their corresponding vertices are adjacent. These touchings also induce the same embedding as in the graph. In a morph between two contact representations we insist that at each time step (continuously throughout the morph) we have a contact representation of the same type. We focus on the case when the geometric objects are triangles that are the lower-right half of axis-parallel rectangles. Such RT-representations exist for every plane graph and right triangles are one of the simplest families of shapes supporting this property. Thus, they provide a natural case to study regarding morphs of contact representations of plane graphs. We study piecewise linear morphs, where each step is a linear morph moving the endpoints of each triangle at constant speed along straight-line trajectories. We provide a polynomial-time algorithm that decides whether there is a piecewise linear morph between two RT-representations of a plane triangulation, and, if so, computes a morph with a quadratic number of linear morphs. As a direct consequence, we obtain that for 4-connected plane triangulations there is a morph between every pair of RT-representations where the ``top-most'' triangle in both representations corresponds to the same vertex. This shows that the realization space of such RT-representations of any 4-connected plane triangulation forms a connected set.</dcterms:abstract> <dc:creator>Angelini, Patrizio</dc:creator> </rdf:Description> </rdf:RDF>

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