Name
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(n 3) area if the triconnected component decomposition tree of G has at most four leaves. In this paper, we improve the area bound O(n 3) to O(n 2), which is optimal up to a constant factor. More precisely, we show that G has a convex grid drawing on a 2n脳4n grid. We also present an algorithm to find such a drawing in linear time. |
Year | DOI | Venue |
|---|---|---|
2009 | 10.1007/978-3-642-10631-6_77 | Discrete Math., Alg. and Appl. |
Keywords | DocType | Volume |
plane graph | Conference | 2 |
Issue | Citations | PageRank |
3 | 0 | 0.34 |
References | Authors | |
9 | 2 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Xiao Zhou | 1 | 325 | 43.69 |
| Takao Nishizeki | 2 | 1771 | 267.08 |