Lecture Notes in Computer Science Volume 1353, 1997, pp 47-51
Date: 29 Jul 2005

Three-dimensional grid drawings of graphs

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A three-dimensional grid drawing of a graph G is a placement of the vertices at distinct integer points so that the straight-line segments representing the edges of G are pairwise non-crossing. It is shown that for any fixed r ≥ 2, every r-colorable graph of n vertices has a three-dimensional grid drawing that fits into a box of volume O(n 2). The order of magnitude of this bound cannot be improved.

Supported by NSF grant CCR-94-24398 and PSC-CUNY Research Award 667339
Supported by the Deutsche Forschungsgemeinschaft
Supported by OTKA-T-020914, OTKA-F-22234 and the Alfred Sloan Foundation