Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the number of edges in a graph with no $(k+1)$-connected subgraphs   Mader proved that for $k\geq 2$ and $n\geq 2k$, every $n$-vertex graph with
no $(k+1)$-connected subgraphs has at most $(1+\frac{1}{\sqrt{2}})k(n-k)$
edges. He also conjectured that for $n$ large with respect to $k$, every such
graph has at most $\frac{3}{2}\left(k - \frac{1}{3}\right)(n-k)$ edges. Yuster
improved Mader's upper bound to $\frac{193}{120}k(n-k)$ for
$n\geq\frac{9k}{4}$. In this note, we make the next step towards Mader's
Conjecture: we improve Yuster's bound to $\frac{19}{12}k(n-k)$ for
$n\geq\frac{5k}{2}$.

4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg