One-Bend Drawings of Outerplanar Graphs Inside Simple Polygons

08/27/2021

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by   Patrizio Angelini, et al.

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We consider the problem of drawing an outerplanar graph with n vertices with at most one bend per edge if the outer face is already drawn as a simple polygon. We prove that it can be decided in O(nm) time if such a drawing exists, where m≤ n-3 is the number of interior edges. In the positive case, we can also compute such a drawing.