## 65 Citations

### The lattice dimension of a tree

- Mathematics
- 2004

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…

### Isometric Diamond Subgraphs

- MathematicsGD
- 2008

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.

### Distance-Balanced Closure of Some Graphs

- 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…

### Drawing a Graph in a Hypercube

- Mathematics, Computer ScienceElectron. 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.

### Cubic Partial Cubes from Simplicial Arrangements

- MathematicsElectron. J. Comb.
- 2006

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.

### 0 Poly-Dimension of Antimatroids

- 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…

### Poly-Dimension of Antimatroids

- 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…

### THE LATTICE DIMENSION OF BENZENOID SYSTEMS

- 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 tree

- Mathematics
- 2004

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…

### An O (N2.5) algorithm for maximum matching in general graphs

- Computer Science16th 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.

### Center and diameter problems in plane triangulations and quadrangulations

- MathematicsSODA '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,…

### Paths, Trees, and Flowers

- MathematicsCanadian Journal of Mathematics
- 1965

A graph G for purposes here is a finite set of elements called vertices and a finite set of elements called edges such that each edge meets exactly two vertices, called the end-points of the edge. An…

### Isometric embedding in products of complete graphs

- Mathematics, Computer ScienceDiscret. Appl. Math.
- 1984

### Embedding Topological Median Algebras in Products of Dendrons

- Mathematics
- 1989

Dendrons and their products admit a natural, continuous median operator. We prove that there exists a two-dimensional metric continuum with a continuous median operator, for which there is no…

### On the Complexity of Recognizing Hamming Graphs and Related Classes of Graphs

- Mathematics, Computer ScienceEur. J. Comb.
- 1996

Abstract This paper contains a new algorithm that recognizes whether a given graph G is a Hamming graph, i.e. a Cartesian product of complete graphs, in O(m) time and O(n 2 ) space. Here m and n…

### Recognizing binary Hamming graphs inO(n2 logn) time

- Computer ScienceMathematical systems theory
- 2005

It is shown that O(n2 logn) time suffices for deciding whether a givenn-vertex graphG is a binary Hamming graph, and for computing a valid addressing scheme forG provided it exists.