We consider three-dimensional grid-drawings of graphs with at most one bend per edge. Under the additional requirement that the vertices be colhnear, we prove that the minimum volume of such a drawing is Θ(cn), where n is the number of vertices and c is the cutwidth of the graph. We then prove that every graph has a three-dimensional grid-drawing with 풪(n3/log2 n) volume and one bend per edge. The best previous bound was 풪(n3).
|Title of host publication||Graph Algorithms and Applications 5|
|Publisher||World Scientific Publishing|
|Number of pages||11|
|ISBN (Print)||981256845X, 9789812568458|
|Publication status||Published - 1 Jan 2006|