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Convex Drawings of Plane Graphs of Minimum Outer Apices

机译:最小外形的平面图的凸图

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In a convex drawing of a plane graph G, every facial cycle of G is drawn as a convex polygon. A polygon for the outer facial cycle is called an outer convex polygon. A necessary and sufficient condition for a plane graph G to have a convex drawing is known. However, it has not been known how many apices of an outer convex polygon are necessary for G to have a convex drawing. In this paper, we show that the minimum number of apices of an outer convex polygon necessary for G to have a convex drawing is, in effect, equal to the number of leaves in a triconnected component decomposition tree of a new graph constructed from G, and that a convex drawing of G having the minimum number of apices can be found in linear time.
机译:在平面图G的凸图中,将G的每个面部周期绘制为凸多边形。外部面部循环的多边形称为外凸多边形。已知平面图G具有凸形图的必要和充分条件。然而,尚不知道G. G的外凸多边形的顶点是多边形的凸形图。在本文中,我们示出了G以具有凸图所需的外凸多边形的最小数量,实际上是等于由G构造的新图形的三角形分组分解树中的叶子的数量等于叶子中所需的叶子的数量。并且可以在线性时间内找到具有最小迹数的G的凸图。

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