Abstract
This paper introduces and studies the concept of a curve embedding of a planar graph. Let \(\mathcal{C}\) be the family of 2D curves described by concave functions and let G be a planar graph. A curve embedding of G is a linear ordering of the vertices of G such that there exists a crossing-free 2D drawing of G where the vertices are constrained to be on any given curve of \(\mathcal{C}\) and the edges are drawn as polylines with at most one bend. We prove that every planar graph has a curve embedding which can be computed in linear time. Further we present applications of the concept of curve embedding to upward drawings and point-set constrained drawings.
Research partially supported by “Progetto ALINWEB: Algoritmica per Internet e per il Web”, MIUR Programmi di Ricerca Scientifica di Rilevante Interesse Nazionale.
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Di Giacomo, E., Didimo, W., Liotta, G., Wismath, S.K. (2003). Drawing Planar Graphs on a Curve. In: Bodlaender, H.L. (eds) Graph-Theoretic Concepts in Computer Science. WG 2003. Lecture Notes in Computer Science, vol 2880. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39890-5_17
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DOI: https://doi.org/10.1007/978-3-540-39890-5_17
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