DIMACS TR: 97-73
Three-dimensional Grid Drawings of Graphs
Authors: János Pach, Torsten Thiele and Géza Tóth
ABSTRACT
A three-dimensional {\em 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 $r\geq
2$, 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.
Paper Available at:
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