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Planar and Quasi Planar Simultaneous Geometric Embeddingwhere Γ. and Γ. are required to be . (i.e., they can have crossings provided that there are no three mutually crossing edges). This relaxation allows for the simultaneous embedding of pairs of planar graphs that are not simultaneously embeddable in the classical SGE setting and opens up to several new interesting research questions.
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https://doi.org/10.1007/978-1-349-21622-2dge has a constant number of bends. If the common graph is biconnected and induced, a straight-line drawing exists. This yields the first efficient testing algorithm for simultaneous geometric embedding (.) for a non-trivial class of graphs.
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https://doi.org/10.1007/978-3-322-85955-6the combinatorial and the algorithmic point of view. We prove tight bounds on the density of constrained versions of fan-planar drawings and study the relationship between fan-planarity and .-planarity. Also, we prove that testing fan-planarity in the variable embedding setting is NP-complete.
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Luatodonotes: Boundary Labeling for Annotations in Textses (straight-line, rectilinear, and Bézier) and modify existing algorithms to allow for annotations of varying height. We have implemented our algorithms in Lua; they are available for download as an easy-to-use Luatex package.
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