Name
Abstract | ||
|---|---|---|
In a convex drawing of a plane graph, all edges are drawn as straight- line segments without any edge-intersection and all facial cycles are drawn as convex polygons. In a convex grid drawing, all vertices are put on grid points. A plane graph G has a convex drawing if and only if G is internally triconnected, and an internally triconnected plane graph G has a convex grid drawing on an (n 1)×(n 1) grid if either G is triconnected or the triconnected component decomposition tree T(G) of G has two or three leaves, where n is the number of vertices in G. In this paper, we show that an internally triconnected plane graph G has a convex grid drawing on a 2n × n2 grid if T(G) has exactly four leaves. We also present an algorithm to find such a drawing in linear time. Our convex grid drawing has a rectangular contour, while most of the known algorithms produce grid drawings having triangular contours. |
Year | Venue | Keywords |
|---|---|---|
2008 | J. Graph Algorithms Appl. | plane graph,linear time |
Field | DocType | Volume |
Orthogonal convex hull,Discrete mathematics,Combinatorics,Convex combination,Convex hull,Convex set,Pseudotriangle,Convex polytope,Steinitz's theorem,Convex curve,Geometry,Mathematics | Journal | 12 |
Issue | Citations | PageRank |
2 | 3 | 0.43 |
References | Authors | |
8 | 3 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Kazuyuki Miura | 1 | 84 | 8.66 |
| Akira Kamada | 2 | 4 | 0.81 |
| Takao Nishizeki | 3 | 1771 | 267.08 |