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1-Planarity of Graphs with a Rotation System
A graph is 1-planar if it can be drawn in the plane such that each edge is crossed at most once. 1-planarity is known NP-hard, even for graphs of bounded bandwidth, pathwidth, or treewidth, and forExpand
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NIC-planar graphs
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 generalizesExpand
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Optical Graph Recognition
Optical graph recognition (OGR) reverses graph drawing. A drawing transforms the topological structure of a graph into a graphical representation. Primarily, it maps vertices to points and displaysExpand
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On the Density of Maximal 1-Planar Graphs
A graph is 1-planar if it can be drawn in the plane such that each edge is crossed at most once. It is maximal 1-planar if the addition of any edge violates 1-planarity. Maximal 1-planar graphsExpand
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Outer 1-Planar Graphs
A graph is outer 1-planar (o1p) if it can be drawn in the plane such that all vertices are in the outer face and each edge is crossed at most once. o1p graphs generalize outerplanar graphs, which canExpand
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Recognizing Outer 1-Planar Graphs in Linear Time
A graph is outer 1-planar o1p if it can be drawn in the plane such that all vertices are on the outer face and each edge is crossed at most once. o1p graphs generalize outerplanar graphs, which canExpand
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Optical Graph Recognition
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Optical Graph Recognition on a Mobile Device
In [1] we proposed Optical Graph Recognition (OGR) as the reversal of graph drawing. A drawing transforms the topological structure of a graph into a graphical representation. Primarily, it mapsExpand