Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Complete subgraphs in multipartite graphs   Turan's Theorem states that every graph of a certain edge density contains a
complete graph $K^k$ and describes the unique extremal graphs. We give a
similar Theorem for l-partite graphs. For large l, we find the minimal edge
density $d^k_l$, such that every $\ell$-partite graph whose parts have pairwise
edge density greater than $d^k_l$ contains a $K^k$. It turns out that
$d^k_l=(k-2)/(k-1)$ for large enough l. We also describe the structure of the
extremal graphs.
  For the case of triangles we show that $d^3_{13}=1/2$, disproving a
conjecture by Bondy, Shen, Thomasse and Thomassen.

31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th