Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Structural properties of bipartite subgraphs   This paper establishes sufficient conditions that force a graph to contain a
bipartite subgraph with a given structural property. In particular, let $\beta$
be any of the following graph parameters: Hadwiger number, Haj\'{o}s number,
treewidth, pathwidth, and treedepth. In each case, we show that there exists a
function $f$ such that every graph $G$ with $\beta(G)\geq f(k)$ contains a
bipartite subgraph $\hat{G}\subseteq G$ with $\beta(\hat{G})\geq k$.

23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph