A star-shaped drawing of a graph is a straight-line drawing such that each inner facial cycle is drawn as a star-shaped polygon, and the outer facial cycle is drawn as a convex polygon. In this paper, given a biconnected planar graph G with fixed plane embedding and a subset A of corners of G, we consider the problem of finding a star-shaped drawing D of G such that only corners in A are allowed to become concave corners in D. We first characterize a necessary and sufficient condition for a subset A of corners to admit such a star-shaped drawing D. Then we present a linear time algorithm for finding such a star-shaped drawing D. Our characterization includes Thomassen's classical characterization of biconnected plane graphs with a prescribed boundary that have convex drawings. © 2008 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Hong, S. H., & Nagamochi, H. (2008). Star-shaped drawings of graphs with fixed embedding and concave corner constraints. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5092 LNCS, pp. 405–414). https://doi.org/10.1007/978-3-540-69733-6_40
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