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On 3-colorings of Plane Graphs
Acta Mathematicae Applicatae Sinica, English Series, 2004The main result of the paper states that any \(3\)-colouring of the vertices of a face of degree at least \(11\) in a planar graph \(G\) without cycles of length \(4\), \(5\) and \(7\) and with no pair of intersecting triangles (i.e. every two 3-cycles of \(G\) are vertex-disjoint) can be extended to a \(3\)-colouring of the whole graph \(G\).
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1992
Planar graphs have many important applications in computer science, for example in VLSI layout. Many problems that are hard or even NP-complete for arbitrary graphs are much easier for planar graphs. In the next lecture we will prove a nice result due to Lipton and Tarjan in 1977 [73] which opens up planar graphs to divide-and-conquer.
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Planar graphs have many important applications in computer science, for example in VLSI layout. Many problems that are hard or even NP-complete for arbitrary graphs are much easier for planar graphs. In the next lecture we will prove a nice result due to Lipton and Tarjan in 1977 [73] which opens up planar graphs to divide-and-conquer.
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2003
Automatic aesthetic drawing of plane graphs has recently created intense interest due to its broad applications, and as a consequence, a number of drawing methods, such as the straight line drawing, convex drawing, orthogonal drawing, rectangular drawing and box-rectangular drawing, have come out [8,9,3,4,5,6,7, 10,11,14,16,23,29,33].
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Automatic aesthetic drawing of plane graphs has recently created intense interest due to its broad applications, and as a consequence, a number of drawing methods, such as the straight line drawing, convex drawing, orthogonal drawing, rectangular drawing and box-rectangular drawing, have come out [8,9,3,4,5,6,7, 10,11,14,16,23,29,33].
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Every outer-1-Plane Graph has a Right Angle Crossing Drawing
International journal of computational geometry and applications, 2012H. R. Dehkordi, P. Eades
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All Separating Triangles in a Plane Graph Can Be Optimally "Broken" in Polynomial Time
International Journal of Foundations of Computer Science, 1999A. Accornero, M. Ancona, Sonia Varini
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Discrete Geometry on Red and Blue Points in the Plane — A Survey —
, 2020A. Kaneko, M. Kano
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Plane Geometric Graph Augmentation: A Generic Perspective
, 2013F. Hurtado, Csaba D. Tóth
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Every planar graph is the intersection graph of segments in the plane: extended abstract
Symposium on the Theory of Computing, 2009Jérémie Chalopin, D. Gonçalves
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CPA-SLAM: Consistent plane-model alignment for direct RGB-D SLAM
IEEE International Conference on Robotics and Automation, 2016Lingni Ma +3 more
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