On Drawing a Graph Convexly in the Plane (Extended Abstract)
Djidjev, Hristo (1995) On Drawing a Graph Convexly in the Plane (Extended Abstract). In: Graph Drawing DIMACS International Workshop, GD 1994, October 10–12, 1994, Princeton, New Jersey, USA , pp. 76-83 (Official URL: http://dx.doi.org/10.1007/3-540-58950-3_358).
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Let G be a planar graph and H be a subgraph of G. Given any convex drawing of H, we investigate the problem of how to extend the drawing of H to a convex drawing of G. We obtain a necessary and sufficient condition for the existence and a linear algorithm for the construction of such an extension. Our results and their corollaries generalize previous theoretical and algorithmic results of Tutte, Thomassen, Chiba, Yamanouchi, and Nishizeki.
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