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Straight-line realization of planar graphs.
, 1971 Few theorems are known about planar graphs. For, example, Kuratowski proved that a graph is planar if and only if it has no subgraph homeomorphic to K₅ or K₃,₃. It has remained as a direct criterion for determining whether a graph is planar or not. Powerful as the theorem is, it is not always easy to apply.
Luang-hung Shiau
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Information Processing Letters, 1998 A simple proof of the representation of bipartite planar graphs as the contact graphs of orthogonal straight line ...
Jurek Czyzowicz +2 more
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Morphing Planar Graph Drawings Through 3D
Conference on Current Trends in Theory and Practice of Informatics, 2022In this paper, we investigate crossing-free 3D morphs between planar straight-line drawings. We show that, for any two (not necessarily topologically equivalent) planar straight-line drawings of an $n$-vertex planar graph, there exists a piecewise-linear
K. Buchin +6 more
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Acute Constraints in Straight-Line Drawings of Planar Graphs
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 2019 Seto Akane +3 more
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Convex Drawings of Hierarchical Graphs in Linear Time, with Applications to Planar Graph Morphing
Embedded Systems and Applications, 2021A hierarchical plane st-graph H can be thought of as a combinatorial description of a planar drawing Γ of a 2-connected graph G in which each edge is a y -monotone curve and each face encloses a y -monotone region (that is, a region whose intersection ...
Boris Klemz
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Straight Line Embeddings of Planar Graphs on Point Sets
, 1996 Netzahualcoyotl Castañeda +1 more
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Planar Straight-Line Embedding of Double-Tree Scan Architecture on a Rectangular Grid
Fundamenta Informaticae, 2008Double-tree-scan (DTS) is a new scan-path architecture that is deemed to be suitable for low-power testing of VLSI circuits. A full DTS resembles two complete k-level (k > 0) binary trees whose leaf nodes are merged pair-wise, and thus consists of ...
I. Saha +3 more
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Morphing Planar Graph Drawings via Orthogonal Box Drawings
International Symposium Graph Drawing and Network VisualizationWe give an algorithm to morph planar graph drawings that achieves small grid size at the expense of allowing a constant number of bends on each edge. The input is an $n$-vertex planar graph and two planar straight-line drawings of the graph on an $O(n ...
Therese Biedl +2 more
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Augmenting the Edge Connectivity of Planar Straight Line Graphs to Three
Algorithmica, 2011We characterize the planar straight line graphs (Pslgs) that can be augmented to 3-connected and 3-edge-connected Pslgs, respectively. We show that if a Pslg with n vertices can be augmented to a 3-edge-connected Pslg, then at most 2n−2 new edges are always sufficient and sometimes necessary for the augmentation.
Mashhood Ishaque +5 more
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