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The number of planar graphs and properties of random planar graphs
Published 2005-01-01Subjects: Get full text
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Random planar graphs
Published 2005“…We study various properties of the random planar graph <em>R<sub>n</sub></em>, drawn uniformly at random from the class <em>P<sub>n</sub></em> of all simple planar graphs on <em>n</em> labelled vertices. …”
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Planar Graphs And Coloring
Published 2010“…Here come the notions of planar graph and the concept of coloring to make the modeling by graphs more efficient.…”
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WORM Colorings of Planar Graphs
Published 2017-05-01“…Given three planar graphs F,H, and G, an (F,H)-WORM coloring of G is a vertex coloring such that no subgraph isomorphic to F is rainbow and no subgraph isomorphic to H is monochromatic. …”
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Triangle Decompositions of Planar Graphs
Published 2016-08-01Subjects: “…planar graphs…”
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Planar Embedding of Planar Graphs
Published 2023“…Valiant [V] gave an algorithm to construct a planar embedding for trees in linear area; he also proved that there are planar graphs that require quadratic area. We fill in a spectrum between Valiant's results by showing that a N-node planar graph has a planar embedding with area O(NF), where F is a bound on the path length from any node to the exterior face. …”
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Random cubic planar graphs.
Published 2007“…We show that the number of labeled cubic planar graphs on n vertices with n even is asymptotically αn-7/2 ρ-nn!…”
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Degree distribution in random planar graphs
Published 2008-01-01Subjects: “…planar graph…”
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Computing The Irregularity Strength of Planar Graphs
Published 2018-08-01Subjects: Get full text
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