Results 21 to 30 of about 892,665 (298)
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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, 2013 In this paper, the concept of Total semirelib graph of a planar graph is introduced. Authors present a characterization of those graphs whose total semirelib graphs are planar, outer planar, Eulerian, hamiltonian with crossing number ...
Prasad, Manjunath +3 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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Planar L-Drawings of Bimodal Graphs
Journal of Graph Algorithms and Applications, 2022 In a planar L-drawing of a directed graph (digraph) each edge $e$ is represented as a polyline composed of a vertical segment starting at the tail of $e$ and a horizontal segment ending at the head of $e$. Distinct edges may overlap, but not cross.
Patrizio Angelini +3 more
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Discrete Applied Mathematics, 2017 A graph is NIC-planar if it admits a drawing in the plane with at most one crossing per edge and such that two pairs of crossing edges share at most one common end vertex. NIC-planarity generalizes IC-planarity, which allows a vertex to be incident to at most one crossing edge, and specializes 1-planarity, which only requires at most one crossing per ...
Christian Bachmaier +4 more
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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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The complexity of two graph orientation problems [PDF]
, 2012 This is the post-print version of the Article. The official published version can be accessed from the link below - Copyright @ 2012 ElsevierWe consider two orientation problems in a graph, namely the minimization of the sum of all the shortest path ...
Noble, Steven D. +7 more
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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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