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

Xiao Zhou, Takao Nishizeki

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)347-362
Number of pages16
JournalDiscrete Mathematics, Algorithms and Applications
Volume2
Issue number3
DOIs
Publication statusPublished - 2010 Sep 1

Keywords

  • Convex drawing
  • plane graph
  • triconnected component decomposition

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

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