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exceptional

Open Rectangle-of-Influence Drawings of Non-triangulated Planar Graphseach edge. Despite recent interest of the graph drawing community in rectangle-of-influence drawings, no algorithm is known to test whether a graph has a planar open weak RI-drawing..In a recent paper, we showed how to test, for inner-triangulated planar graphs, whether they have a planar open weak

helper-T-cells

水獭

Planar Lombardi Drawings for Subcubic Graphss around every vertex. Our construction is based on the Koebe–Andreev–Thurston circle packing theorem, and uses a novel type of Voronoi diagram for circle packings that is invariant under Möbius transformations, defined using three-dimensional hyperbolic geometry. We also use circle packing to const

乐章

Inoperable

反叛者

Planar Graphs as VPG-Graphsgraphs are ..-VPG and this was conjectured to be tight. We disprove this conjecture by showing that all planar graphs are ..-VPG. We also show that the 4-connected planar graphs are a subclass of the intersection graphs of Z-shapes (i.e., a special case of ..-VPG). Additionally, we demonstrate that

corn732

On Representing Graphs by Touching Cuboidsare represented by a proper contact between the cuboids representing their endvertices. Two cuboids make a proper contact if they intersect and their intersection is a non-zero area rectangle contained in the boundary of both. We study representations where all cuboids are unit cubes, where they are

outset

Bridle

沉着

Counting Plane Graphs: Cross-Graph Charging Schemes the set of all crossing-free straight-edge graphs that can be embedded over a specific point set..We then show how to apply the cross-graph charging-scheme method for graphs that allow certain types of crossings. Specifically, we consider graphs with no set of . pairwise-crossing edges (more common