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Algorithms and Bounds for Drawing Non-planar Graphs with Crossing-free Subgraphs

We initiate the study of the following problem: Given a non-planar graph G and a planar subgraph S of G, does there exist a straight-line drawing Γ of G in the plane such that the edges of S are not crossed in Γ by any edge of G? We give positive and negative results for different kinds of connected spanning subgraphs S of G. Moreover, in order to enlarge the subset of instances that admit a solution, we consider the possibility of bending the edges of G not in S; in this setting we discuss different trade-offs between the number of bends and the required drawing area.

preprint2014arXivOpen access
Patrizio AngeliniCarla BinucciGiordano Da LozzoWalter DidimoLuca GrilliFabrizio MontecchianiMaurizio PatrignaniIoannis G. Tollis
Computational Geometry
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Open access8 authors1 topic
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Patrizio AngeliniCarla BinucciGiordano Da LozzoWalter DidimoLuca GrilliFabrizio MontecchianiMaurizio PatrignaniIoannis G. Tollis

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