Grid Embedding of 4-Connected Plane Graphs
He, Xin (1996) Grid Embedding of 4-Connected Plane Graphs. In: Symposium on Graph Drawing, GD 1995, September 20-22, 1995, Passau, Germany , pp. 287-299 (Official URL: http://dx.doi.org/10.1007/BFb0021812).
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A straight line grid embedding of a plane graph G is a drawing of G such that the vertices are drawn at grid points and the edges are drawn as non-intersecting straight line segments. In this paper, we show that, if a 4-connected plane graph G has at least 4 vertices on its exterior face, then G can be embedded on a grid of size W \times H such that W + H \le n, W \le (n + 3)/2 and H \le 2(n - 1)/3, where n is the number of vertices of G. Such an embedding can be computed in linear time.
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