Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dense induced subgraphs of dense bipartite graphs   We prove that every bipartite graph of sufficiently large average degree has
either a $K_{t,t}$-subgraph or an induced subgraph of average degree at least
$t$ and girth at least $6$. We conjecture that "$6$" can be replaced by "$k$",
which strengthens a conjecture of Thomassen. In support of this conjecture, we
show that it holds for regular graphs.

13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg