Hanani-Tutte and Monotone Drawings
Identifieur interne : 000472 ( Main/Exploration ); précédent : 000471; suivant : 000473Hanani-Tutte and Monotone Drawings
Auteurs : Radoslav Fulek [Suisse] ; J. Pelsmajer [États-Unis] ; Marcus Schaefer [États-Unis] ; Daniel Štefankovi [États-Unis]Source :
- Lecture Notes in Computer Science [ 0302-9743 ] ; 2011.
Abstract
Abstract: A drawing of a graph is x-monotone if every edge intersects every vertical line at most once and every vertical line contains at most one vertex. Pach and Tóth showed that if a graph has an x-monotone drawing in which every pair of edges crosses an even number of times, then the graph has an x-monotone embedding in which the x-coordinates of all vertices are unchanged. We give a new proof of this result and strengthen it by showing that the conclusion remains true even if adjacent edges are allowed to cross oddly. This answers a question posed by Pach and Tóth. Moreover, we show that an extension of this result for graphs with non-adjacent pairs of edges crossing oddly fails even if there exists only one such pair in a graph.
Url:
DOI: 10.1007/978-3-642-25870-1_26
Affiliations:
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Pelsmajer</name></author><author><name sortKey="Schaefer, Marcus" sort="Schaefer, Marcus" uniqKey="Schaefer M" first="Marcus" last="Schaefer">Marcus Schaefer</name></author><author><name sortKey="Stefankovi, Daniel" sort="Stefankovi, Daniel" uniqKey="Stefankovi D" first="Daniel" last="Štefankovi">Daniel Štefankovi</name></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:3FB5EBB34A3D578BC4F6F9BB274A78CF498BD1E9</idno><date when="2011" year="2011">2011</date><idno type="doi">10.1007/978-3-642-25870-1_26</idno><idno type="url">https://api.istex.fr/document/3FB5EBB34A3D578BC4F6F9BB274A78CF498BD1E9/fulltext/pdf</idno><idno type="wicri:Area/Istex/Corpus">000779</idno><idno type="wicri:Area/Istex/Curation">000770</idno><idno type="wicri:Area/Istex/Checkpoint">000129</idno><idno type="wicri:doubleKey">0302-9743:2011:Fulek R:hanani:tutte:and</idno><idno type="wicri:Area/Main/Merge">000478</idno><idno type="wicri:Area/Main/Curation">000472</idno><idno type="wicri:Area/Main/Exploration">000472</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">Hanani-Tutte and Monotone Drawings</title><author><name sortKey="Fulek, Radoslav" sort="Fulek, Radoslav" uniqKey="Fulek R" first="Radoslav" last="Fulek">Radoslav Fulek</name><affiliation wicri:level="3"><country xml:lang="fr">Suisse</country><wicri:regionArea>Ecole Polytechnique Fédérale de Lausanne, Lausanne</wicri:regionArea><placeName><settlement type="city">Lausanne</settlement><region nuts="3" type="region">Canton de Vaud</region></placeName></affiliation><affiliation wicri:level="1"><country wicri:rule="url">Suisse</country></affiliation></author><author><name sortKey="Pelsmajer, J" sort="Pelsmajer, J" uniqKey="Pelsmajer J" first="J." last="Pelsmajer">J. 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Pach and Tóth showed that if a graph has an x-monotone drawing in which every pair of edges crosses an even number of times, then the graph has an x-monotone embedding in which the x-coordinates of all vertices are unchanged. We give a new proof of this result and strengthen it by showing that the conclusion remains true even if adjacent edges are allowed to cross oddly. This answers a question posed by Pach and Tóth. Moreover, we show that an extension of this result for graphs with non-adjacent pairs of edges crossing oddly fails even if there exists only one such pair in a graph.</div></front></TEI><affiliations><list><country><li>Suisse</li><li>États-Unis</li></country><region><li>Canton de Vaud</li><li>Illinois</li><li>État de New York</li></region><settlement><li>Lausanne</li></settlement></list><tree><country name="Suisse"><region name="Canton de Vaud"><name sortKey="Fulek, Radoslav" sort="Fulek, Radoslav" uniqKey="Fulek R" first="Radoslav" last="Fulek">Radoslav Fulek</name></region><name sortKey="Fulek, Radoslav" sort="Fulek, Radoslav" uniqKey="Fulek R" first="Radoslav" last="Fulek">Radoslav Fulek</name></country><country name="États-Unis"><region name="Illinois"><name sortKey="Pelsmajer, J" sort="Pelsmajer, J" uniqKey="Pelsmajer J" first="J." last="Pelsmajer">J. Pelsmajer</name></region><name sortKey="Pelsmajer, J" sort="Pelsmajer, J" uniqKey="Pelsmajer J" first="J." last="Pelsmajer">J. Pelsmajer</name><name sortKey="Schaefer, Marcus" sort="Schaefer, Marcus" uniqKey="Schaefer M" first="Marcus" last="Schaefer">Marcus Schaefer</name><name sortKey="Schaefer, Marcus" sort="Schaefer, Marcus" uniqKey="Schaefer M" first="Marcus" last="Schaefer">Marcus Schaefer</name><name sortKey="Stefankovi, Daniel" sort="Stefankovi, Daniel" uniqKey="Stefankovi D" first="Daniel" last="Štefankovi">Daniel Štefankovi</name><name sortKey="Stefankovi, Daniel" sort="Stefankovi, Daniel" uniqKey="Stefankovi D" first="Daniel" last="Štefankovi">Daniel Štefankovi</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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