Results 11 to 20 of about 29,288 (268)
On the planarity of line Mycielskian graph of a graph
Ratio Mathematica, 2020 The line Mycielskian graph of a graph G, denoted by Lμ(G) is defined as the graph obtained from L(G) by adding q+1 new vertices E' = ei' : 1 ≤ i ≤ q and e, then for 1 ≤ i ≤ q , joining ei' to the neighbours of ei and to e.
Keerthi G. Mirajkar +1 more
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On the planar edge-length ratio of planar graphs
Journal of Computational Geometry, 2020 The edge-length ratio of a straight-line drawing of a graph is the ratio between the lengths of the longest and of the shortest edge in the drawing. The planar edge-length ratio of a planar graph is the minimum edge-length ratio of any planar straight ...
Manuel Borrazzo, Fabrizio Frati
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An SPQR-tree-like embedding representation for level planarity
Journal of Computational Geometry, 2023 An SPQR-tree is a data structure that efficiently represents all planar embeddings of a connected planar graph. It is a key tool in a number of constrained planarity testing algorithms, which seek a planar embedding of a graph subject to some given set
Guido Brückner, Ignaz Rutter
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Upward Planar Drawings with Three and More Slopes
Journal of Graph Algorithms and Applications, 2023 The slope number of a graph $G$ is the smallest number of slopes needed for the segments representing the edges in any straight-line drawing of $G$. It serves as a measure of the visual complexity of a graph drawing.
Jonathan Klawitter, Johannes Zink
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Connectivity of Planar Graphs [PDF]
Journal of Graph Algorithms and Applications, 2001 We give here three simple linear time algorithms on planar graphs: a 4-connexity test for maximal planar graphs, an algorithm enumerating the triangles and a 3-connexity test. Although all these problems got already linear-time solutions, the presented algorithms are both simple and efficient. They are based on some new theoretical results.
de Fraysseix, Hubert +1 more
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Drawing planar graphs with many collinear vertices
Journal of Computational Geometry, 2018 Consider the following problem: Given a planar graph $G$, what is the maximum number $p$ such that $G$ has a planar straight-line drawing with $p$ collinear vertices?
Giordano Da Lozzo +4 more
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Theoretical Computer Science, 2018 We introduce the family of $k$-gap-planar graphs for $k \geq 0$, i.e., graphs that have a drawing in which each crossing is assigned to one of the two involved edges and each edge is assigned at most $k$ of its crossings. This definition is motivated by applications in edge casing, as a $k$-gap-planar graph can be drawn crossing-free after introducing ...
Sang Won Bae 0001 +10 more
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Matched Drawings of Planar Graphs
Journal of Graph Algorithms and Applications, 2009 A natural way to draw two planar graphs whose vertex sets are matched is to assign each matched pair a unique y-coordinate. In this paper we introduce the concept of such matched drawings, which is a relaxation of simultaneous geometric embeddings with ...
Emilio Di Giacomo +4 more
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Improved Bounds for Track Numbers of Planar Graphs
Journal of Graph Algorithms and Applications, 2020 A track layout of a graph consists of a vertex coloring and a total order of each color class, such that no two edges cross between any two color classes.
Sergey Pupyrev
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Box-Rectangular Drawings of Planar Graphs
Journal of Graph Algorithms and Applications, 2013 A plane graph is a planar graph with a fixed planar embedding in the plane. In a box- rectangular drawing of a plane graph, every vertex is drawn as a rectangle, called a box, each edge is drawn as either a horizontal line segment or a vertical line ...
Md. Manzurul Hasan +2 more
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