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cs.DSFeb 13, 2004
63
citations (OpenAlex)
authors
  • David Eppstein
institutions
  • University of California, Irvine
arXiv abstractPDF
paper

The lattice dimension of a graph

arXiv:cs/0402028 · doi:10.1016/j.ejc.2004.05.001

Abstract

We describe a polynomial time algorithm for, given an undirected graph G, finding the minimum dimension d such that G may be isometrically embedded into the d-dimensional integer lattice Z^d.

6 pages, 3 figures

References in corpus (1)

  • The lattice dimension of a tree

Cited by in corpus (16)

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  • Recognizing Partial Cubes in Quadratic Time
  • Steinitz Theorems for Orthogonal Polyhedra
  • The lattice dimension of a tree
  • Shortest path problem in rectangular complexes of global nonpositive curvature
  • On partial cubes, well-graded families and their duals with some applications in graphs
  • Isometric embeddings in trees and their use in the diameter problem
  • On the Medianwidth of Graphs
  • Cops, Robber and Medianwidth Parameters
  • Isometric Diamond Subgraphs
  • The Fibonacci dimension of a graph
  • Cubic Partial Cubes from Simplicial Arrangements
  • Algorithms for Drawing Media
  • Partial cubes: structures, characterizations, and constructions
  • Upright-Quad Drawing of st-Planar Learning Spaces
  • Drawing a Graph in a Hypercube
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