Journal of Graph Algorithms and Applications
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Convex Grid Drawings of Plane Graphs with Rectangular Contours
Vol. 12, no. 2, pp. 197-224, 2008. Regular paper.
Abstract In a convex drawing of a plane graph, all edges are drawn as straight-line segments without any edge-intersection and all facial cycles are drawn as convex polygons. In a convex grid drawing, all vertices are put on grid points. A plane graph G has a convex drawing if and only if G is internally triconnected, and an internally triconnected plane graph G has a convex grid drawing on an (n−1) ×(n−1) grid if either G is triconnected or the triconnected component decomposition tree T(G) of G has two or three leaves, where n is the number of vertices in G. In this paper, we show that an internally triconnected plane graph G has a convex grid drawing on a 2n ×n2 grid if T(G) has exactly four leaves. We also present an algorithm to find such a drawing in linear time. Our convex grid drawing has a rectangular contour, while most of the known algorithms produce grid drawings having triangular contours.
Submitted: August 2007.
Reviewed: June 2008.
Revised: July 2008.
Accepted: July 2008.
Final: July 2008.
Published: October 2008.
Communicated by Xin He