首页> 外文期刊>Journal of Combinatorial Optimization >Small grid drawings of planar graphs with balanced partition
【24h】

Small grid drawings of planar graphs with balanced partition

机译:具有平衡分区的平面图的小网格图

获取原文
获取原文并翻译 | 示例

摘要

In a grid drawing of a planar graph, every vertex is located at a grid point, and every edge is drawn as a straight-line segment without any edge-intersection. It is known that every planar graph G of n vertices has a grid drawing on an (n−2)×(n−2) or (4n/3)×(2n/3) integer grid. In this paper we show that if a planar graph G has a balanced partition then G has a grid drawing with small grid area. More precisely, if a separation pair bipartitions G into two edge-disjoint subgraphs G 1 and G 2, then G has a max {n 1,n 2}×max {n 1,n 2} grid drawing, where n 1 and n 2 are the numbers of vertices in G 1 and G 2, respectively. In particular, we show that every series-parallel graph G has a (2n/3)×(2n/3) grid drawing and a grid drawing with area smaller than 0.3941n 2 (<(2/3)2 n 2).
机译:在平面图的网格图中,每个顶点都位于一个网格点,并且每个边缘都绘制为直线段,而没有任何边缘相交。已知n个顶点的每个平面图G在(n-2)×(n-2)或(4n / 3)×(2n / 3)整数网格上具有网格图。在本文中,我们表明,如果平面图G具有平衡的分区,则G的网格图的网格面积较小。更准确地说,如果分隔对将G分成两个边不相交的子图G 1 和G 2 ,则G的最大值为{n 1 ,n 2 }×max {n 1 ,n 2 }网格图,其中n 1 和n < sub> 2 分别是G 1 和G 2 中的顶点数。尤其是,我们证明每个串并联图G都有一个(2n / 3)×(2n / 3)网格图和一个面积小于0.3941n 2 (<(2 / 3) 2 n 2 )。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱:kefu@zhangqiaokeyan.com

京公网安备:11010802029741号 ICP备案号:京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有
  • 客服微信

  • 服务号