Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Tight Bound for Minimal Connectivity   For minimally $k$-connected graphs on $n$ vertices, Mader proved a tight
lower bound for the number $|V_k|$ of vertices of degree $k$ in dependence on
$n$ and $k$. Oxley observed 1981 that in many cases a considerably better bound
can be given if $m := |E|$ is used as additional parameter, i.e. in dependence
on $m$, $n$ and $k$. It was left open to determine whether Oxley's bound is
best possible.
  We show that this is not the case, but propose a closely related bound that
deviates from Oxley's long-standing one only for small values of $m$. We prove
that this new bound is best possible. The bound contains Mader's bound as
special case.

24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc