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2003
Springer

Three-Dimensional Grid Drawings with Sub-quadratic Volume

9 years 2 months ago
Three-Dimensional Grid Drawings with Sub-quadratic Volume
A three-dimensional grid drawing of a graph is a placement of the vertices at distinct points with integer coordinates, such that the straight line-segments representing the edges are pairwise non-crossing. A O(n3/2) volume bound is proved for three-dimensional grid drawings of graphs with bounded degree, graphs with bounded genus, and graphs with no bounded complete graph as a minor. The previous best bound for these graph families was O(n2). These results (partially) solve open problems due to Pach, Thiele, and T´oth (1997) and Felsner, Liotta, and Wismath (2001).
Vida Dujmovic, David R. Wood
Added 06 Jul 2010
Updated 06 Jul 2010
Type Conference
Year 2003
Where GD
Authors Vida Dujmovic, David R. Wood
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