Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Large complete minors in random subgraphs   Let $G$ be a graph of minimum degree at least $k$ and let $G_p$ be the random
subgraph of $G$ obtained by keeping each edge independently with probability
$p$. We are interested in the size of the largest complete minor that $G_p$
contains when $p = \frac{1+\varepsilon}{k}$ with $\varepsilon >0$. We show that
with high probability $G_p$ contains a complete minor of order
$\tilde{\Omega}(\sqrt{k})$, where the $\sim$ hides a polylogarithmic factor.
Furthermore, in the case where the order of $G$ is also bounded above by a
constant multiple of $k$, we show that this polylogarithmic term can be
removed, giving a tight bound.

35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ