Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Embedding products of graphs into Euclidean spaces   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 is the join of n copies of a 4-point
set, has a pair of linked (n-1)-dimensional spheres.

22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th