Convex drawings of internally triconnected plane graphs on O(n2) grids

Xiao Zhou, Takao Nishizeki

研究成果: Article査読

3 被引用数 (Scopus)

抄録

In a convex grid drawing of a plane graph, every edge is drawn as a straight-line segment without any edge-intersection, every vertex is located at a grid point, and every facial cycle is drawn as a convex polygon. A plane graph G has a convex drawing if and only if G is internally triconnected. It has been known that an internally triconnected plane graph G of n vertices has a convex grid drawing on a grid of O(n3) area if the triconnected component decomposition tree of G has at most four leaves. In this paper, we improve the area bound O(n3) to O(n2), which is optimal up to a constant factor. More precisely, we show that G has a convex grid drawing on a 2n × 4n grid. We also present an algorithm to find such a drawing in linear time.

本文言語English
ページ(範囲)347-362
ページ数16
ジャーナルDiscrete Mathematics, Algorithms and Applications
2
3
DOI
出版ステータスPublished - 2010 9 1

ASJC Scopus subject areas

  • 離散数学と組合せ数学

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