Grid Drawings of Four-Connected Plane Graphs
Miura, Kazuyuki and Nakano, Shin-Ichi and Nishizeki, Takao (1999) Grid Drawings of Four-Connected Plane Graphs. In: Graph Drawing 7th International Symposium, GD’99, September 15-19, 1999, Štirín Castle, Czech Republic , pp. 145-154 (Official URL: http://dx.doi.org/10.1007/3-540-46648-7_15).
Full text not available from this repository.
A grid drawing of a plane graph G is a drawing of G on the plane so that all vertices of G are put on plane grid points and all edges are drawn as straight line segments between their endpoints without any edge-intersection. In this paper we give a very simple algorithm to find a grid drawing of any given 4-connected plane graph G with four or more vertices on the outer face. The algorithm takes time O(n) and needs a rectangular grid of width \lceil n/2 \rceil - 1 and height \lceil n/2 \rceil if G has n vertices. The algorithm is best possible in the sense that there are an infinite number of 4-connected plane graphs any grid drawings of which need rectangular grids of width \lceil n/2 \rceil - 1 and height \lceil n/2 \rceil.
Repository Staff Only: item control page