Embedding products of graphs into Euclidean spaces

@article{Skopenkov2003EmbeddingPO,
  title={Embedding products of graphs into Euclidean spaces},
  author={M. Skopenkov},
  journal={arXiv: Geometric Topology},
  year={2003}
}
  • M. Skopenkov
  • Published 2003
  • Mathematics
  • arXiv: Geometric Topology
For any collection of graphs we find the minimal dimension d such that the product of these graphs is embeddable into the d-dimensional Euclidean space. In particular, we prove that the n-th powers of the Kuratowsky graphs are not embeddable into the 2n-dimensional Euclidean space. This is a solution of a problem of Menger from 1929. The idea of the proof is the reduction to a problem from so-called Ramsey link theory: we show that any embedding of L into the (2n-1)-dimensional sphere, where L… Expand
21 Citations

Figures from this paper

On the Links of Vertices in Simplicial d-Complexes Embeddable in the Euclidean 2d-Space
  • S. Parsa
  • Mathematics, Computer Science
  • Discret. Comput. Geom.
  • 2018
  • 8
  • PDF
Combinatorics of embeddings
  • 9
  • PDF
Invariants of Graph Drawings in the Plane
  • 7
  • Highly Influenced
  • PDF
Some short proofs of the nonrealizability of hypergraphs
  • 8
  • Highly Influenced
Multibranched surfaces in 3-manifolds.
  • Highly Influenced
  • PDF
...
1
2
3
...

References

SHOWING 1-10 OF 54 REFERENCES
...
1
2
3
4
5
...