How to use planarly in a sentence? Find typical usage patterns (collocations)/phrases/context for "planarly" and check conjugation/comparative form for "planarly". Mastering all the usages of "planarly" from sentence examples published by news publications.
Although the colors in the painting are still lovely, they lack the vivid contrast which makes The Idiot so memorable. Instead of playing off of opposite colors, O Canal e a Ponta is one swell of deep shades that vary slightly from light reflections. The painting is still beautiful, it is simply much more traditional. The style is much more reminiscent of a toned down expressionism and does not utilise any qualities of Cubism which made her first pieces so planarly abstract.
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It is NP-complete to test whether a given graph is 1-planar,.. and it remains NP-complete even for the graphs formed from planar graphs by adding a single edge. Expanded version of a paper from the 17th ACM Symposium on Computational Geometry, 2010. and for graphs of bounded bandwidth.. The problem is fixed-parameter tractable when parameterized by cyclomatic number or by tree-depth, so it may be solved in polynomial time when those parameters are bounded. In contrast to Fáry's theorem for planar graphs, not every 1-planar graph may be drawn 1-planarly with straight line segments for its edges... However, testing whether a 1-planar drawing may be straightened in this way can be done in polynomial time.. Additionally, every 3-vertex-connected 1-planar graph has a 1-planar drawing in which at most one edge, on the outer face of the drawing, has a bend in it.
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Simultaneous embedding is a technique in graph drawing and information visualization for visualizing two or more different graphs on the same or overlapping sets of labeled vertices, while avoiding crossings within both graphs. Crossings between an edge of one graph and an edge of the other graph are allowed. If edges are allowed to be drawn as polylines or curves, then any planar graph may be drawn without crossing its vertices in arbitrary positions in the plane, where the same vertex placement provides a simultaneous embedding. There are two restricted models: simultaneous geometric embedding, where each graph must be drawn planarly with line segments representing its edges rather than more complex curves restricting the two given graphs to subclasses of the planar graphs and simultaneous embedding with fixed edges, where curves or bends are allowed in the edges, but any edge in both graphs must be represented by the same curve in both drawings.
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Minimizing the number of crossings is NP-complete, but may be approximated with an approximation ratio of where is the number of vertices.. Minimizing the one- page or two-page crossing number is fixed-parameter tractable when parameterized by the cyclomatic number of the given graph, or by a combination of the crossing number and the treewidth of the graph... Heuristic methods for reducing the crossing complexity have also been devised, based e.g. on a careful vertex insertion order and on local optimization. Two-page book embeddings with a fixed partition of the edges into pages can be interpreted as a form of clustered planarity, in which the given graph must be drawn in such a way that parts of the graph (the two subsets of edges) are placed in the drawing in a way that reflects their clustering. Two-page book embedding has also been used to find simultaneous embeddings of graphs, in which two graphs are given on the same vertex set and one must find a placement for the vertices in which both graphs are drawn planarly with straight edges.. Book embeddings with more than two pages have also been used to construct three- dimensional drawings of graphs.
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