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• W2096978969 abstract "A drawing of a graph is a monotone drawing if for every pair of vertices u and v there is a path drawn from u to v that is monotone in some direction. In this paper we investigate planar monotone drawings in the fixed embedding setting, i.e., a planar embedding of the graph is given as part of the input that must be preserved by the drawing algorithm. In this setting we prove that every planar graph on n vertices admits a planar monotone drawing with at most two bends per edge and with at most 4n−10 bends in total; such a drawing can be computed in linear time and requires polynomial area. We also show that two bends per edge are sometimes necessary on a linear number of edges of the graph. Furthermore, we investigate subclasses of planar graphs that can be realized as embedding-preserving monotone drawings with straight-line edges. In fact, we prove that biconnected embedded planar graphs and outerplane graphs always admit such drawings, and describe linear-time drawing algorithms for these two graph classes." @default.
• W2096978969 created "2016-06-24" @default.
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• W2096978969 date "2013-05-03" @default.
• W2096978969 modified "2023-10-16" @default.
• W2096978969 title "Monotone Drawings of Graphs with Fixed Embedding" @default.
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• W2096978969 doi "https://doi.org/10.1007/s00453-013-9790-3" @default.
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