Drawings in the Air

Graph Drawing

Volume 1353 of the series Lecture Notes in Computer Science pp 47-51

Date:

Three-dimensional grid drawings of graphs

  • János PachAffiliated withCourant Institute, New York University
  • , Torsten ThieleAffiliated withCourant Institute, New York University
  • , Géza TóthAffiliated withCourant Institute, New York University

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Abstract

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.