Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The domination number of the graph defined by two levels of the
  $n$-cube, II   Consider all $k$-element subsets and $\ell$-element subsets $(k>\ell )$ of an
$n$-element set as vertices of a bipartite graph. Two vertices are adjacent if
the corresponding $\ell$-element set is a subset of the corresponding
$k$-element set. Let $G_{k,\ell}$ denote this graph. The domination number of
$G_{k,1}$ was exactly determined by Badakhshian, Katona and Tuza. A conjecture
was also stated there on the asymptotic value ($n$ tending to infinity) of the
domination number of $G_{k,2}$. Here we prove the conjecture, determining the
asymptotic value of the domination number $\gamma (G_{k,2})={k+3\over
2(k-1)(k+1)}n^2+o(n^2)$.

35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th