Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tiling tripartite graphs with 3-colorable graphs: The extreme case   There is a sufficiently large $N\in h\mathbb{N}$ such that the following
holds. If $G$ is a tripartite graph with $N$ vertices in each vertex class such
that every vertex is adjacent to at least $2N/3+2h-1$ vertices in each of the
other classes, then $G$ can be tiled perfectly by copies of $K_{h,h,h}$. This
extends work by two of the authors [Electron. J. Combin, 16(1), 2009] and also
gives a sufficient condition for tiling by any fixed 3-colorable graph.
Furthermore, we show that $2N/3+2h-1$ in our result can not be replaced by
$2N/3+ h-2$ and that if $N$ is divisible by $6h$, then we can replace it with
the value $2N/3+h-1$ and this is tight.

24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc