Abstract
A straight-line drawing of a plane graph is called an open rectangle-of-influence drawing if there is no vertex in the proper inside of the axis-parallel rectangle defined by the two ends of every edge. In an inner triangulated plane graph, every inner face is a triangle although the outer face is not necessarily a triangle. In this paper, we first obtain a sufficient condition for an inner triangulated plane graph G to have an open rectangle-of-influence drawing; the condition is expressed in terms of a labeling of angles of a subgraph of G. We then present an O(n 1.5/log n)-time algorithm to examine whether G satisfies the condition and, if so, construct an open rectangle-of-influence drawing of G on an (n−1)×(n−1) integer grid, where n is the number of vertices in G.
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Miura, K., Matsuno, T. & Nishizeki, T. Open Rectangle-of-Influence Drawings of Inner Triangulated Plane Graphs. Discrete Comput Geom 41, 643–670 (2009). https://doi.org/10.1007/s00454-008-9098-2
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DOI: https://doi.org/10.1007/s00454-008-9098-2