# The lattice dimension of a graph

```@article{Eppstein2004TheLD,
title={The lattice dimension of a graph},
author={David Eppstein},
journal={ArXiv},
year={2004},
volume={cs.DS/0402028}
}```
• D. Eppstein
• Published 12 February 2004
• Mathematics, Computer Science
• ArXiv
65 Citations

## Figures from this paper

The lattice dimension of a graph G is the minimal dimension of a cubic lattice in which G can be isometrically embedded. We prove that the lattice dimension of a tree with n leaves is \$\lceil n/2
• Mathematics, Computer Science
Eur. J. Comb.
• 2009
We test in polynomial time whether a graph embeds in a distance-preserving way into the hexagonal tiling, the three-dimensional diamond structure, or analogous higher-dimensional structures.
• Mathematics
• 2010
In this paper we prove that any distance-balanced graph G with �(G) � jV (G)j −3 is regular. Also we define notion of distance- balanced closure of a graph and we find distance-balanced closures of
• D. Wood
• Mathematics, Computer Science
Electron. J. Comb.
• 2006
Lower and upper bounds on the minimum number of dimensions in hypercube drawing of a given graph are studied and this parameter turns out to be related to Sidon sets and antimagic injections.
It is shown how to construct a cubic partial cube from any simplicial arrangement of lines or pseudolines in the projective plane and nine new infinite families of cubic partial cubes are found.
A partial cube is a graph that can be isometrically embedded into a hypercube. In other words, a partial cube is a subgraph of a hypercube that preserves distances the distance between any two
• Mathematics
• 2012
A partial cube is a graph that can be isometrically embedded into a hypercube. In other words, a partial cube is a subgraph of a hypercube that preserves distances the distance between any two
• Computer Science
• 2006
A labeling of vertices of a benzenoid system B is proposed that reflects the graph distance in B and is significantly shorter that the labeling obtained from a hypercube embedding of B. The new

## References

SHOWING 1-10 OF 17 REFERENCES

The lattice dimension of a graph G is the minimal dimension of a cubic lattice in which G can be isometrically embedded. We prove that the lattice dimension of a tree with n leaves is \$\lceil n/2
• Computer Science
16th Annual Symposium on Foundations of Computer Science (sfcs 1975)
• 1975
This work presents a new efficient algorithm for finding a maximum matching in an arbitrary graph that is O(m√n¿log n) where n, m are the numbers of the vertices and the edges in the graph.
• Mathematics
SODA '02
• 2002
In this note, we present first linear time algorithms for computing the center and the diameter of several classes of face regular plane graphs: triangulations with inner vertices of degree ≥ 6,
• J. Edmonds
• Mathematics