Abstract
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(n 3/2) 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 Tóth [Graph Drawing 1997] and Felsner, Liotta, and Wismath [Graph Drawing 2001]. © Springer-Verlag 2004.
Cite
CITATION STYLE
Dujmović, V., & Wood, D. R. (2004). Three-Dimensional Grid Drawings with Sub-quadratic Volume. Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2912, 190–201. https://doi.org/10.1007/978-3-540-24595-7_18
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