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 2 n × n 2 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.
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