Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Characterizations of minimal graphs with equal edge connectivity and
  spanning tree packing number   With graphs considered as natural models for many network design problems,
edge connectivity $\kappa'(G)$ and maximum number of edge-disjoint spanning
trees $\tau(G)$ of a graph $G$ have been used as measures for reliability and
strength in communication networks modeled as graph $G$ (see \cite{Cunn85,
Matula87}, among others). Mader \cite{Mader71} and Matula \cite{Matula72}
introduced the maximum subgraph edge connectivity $\overline{\kappa'}(G)=\max
\{\kappa'(H): H \mbox{ is a subgraph of } G \}$. Motivated by their
applications in network design and by the established inequalities \[
\overline{\kappa'}(G)\ge \kappa'(G) \ge \tau(G), \] we present the following in
this paper:
  (i) For each integer $k>0$, a characterization for graphs $G$ with the
property that $\overline{\kappa'}(G) \le k$ but for any edge $e$ not in $G$,
$\overline{\kappa'}(G+e)\ge k+1$.
  (ii) For any integer $n > 0$, a characterization for graphs $G$ with $|V(G)|
= n$ such that $\kappa'(G) = \tau(G)$ with $|E(G)|$ minimized.

7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex