• DOI:10.4064/FM179-3-1
Corpus ID: 15760414

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

View PDF on arXiv

Save to Library

Create Alert

Cite

Launch Research Feed