Results 21 to 30 of about 975,712 (248)
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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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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Untangling a Planar Graph [PDF]
Discrete & Computational Geometry, 2008 A straight-line drawing $δ$ of a planar graph $G$ need not be plane, but can be made so by \emph{untangling} it, that is, by moving some of the vertices of $G$. Let shift$(G,δ)$ denote the minimum number of vertices that need to be moved to untangle $δ$. We show that shift$(G,δ)$ is NP-hard to compute and to approximate.
Xavier Goaoc +5 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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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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Minimizing the oriented diameter of a planar graph [PDF]
, 2009 We consider the problem of minimizing the diameter of an orientation of a planar graph. A result of Chvátal and Thomassen shows that for general graphs, it is NP-complete to decide whether a graph can be oriented so that its diameter is at most two.
Noble, SD +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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The Liouville and the intersection properties are equivalent for planar graphs [PDF]
, 2012 It is shown that if a planar graph admits no non-constant bounded harmonic function then the trajectories of two independent simple random walks intersect almost ...
Itai Benjamini +5 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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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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