Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nordhaus-Gaddum-type results for the generalized edge-connectivity of
  graphs   Let $G$ be a graph, $S$ be a set of vertices of $G$, and $\lambda(S)$ be the
maximum number $\ell$ of pairwise edge-disjoint trees $T_1, T_2,..., T_{\ell}$
in $G$ such that $S\subseteq V(T_i)$ for every $1\leq i\leq \ell$. The
generalized $k$-edge-connectivity $\lambda_k(G)$ of $G$ is defined as
$\lambda_k(G)= min\{\lambda(S) | S\subseteq V(G) \ and \ |S|=k\}$. Thus
$\lambda_2(G)=\lambda(G)$. In this paper, we consider the Nordhaus-Gaddum-type
results for the parameter $\lambda_k(G)$. We determine sharp upper and lower
bounds of $\lambda_k(G)+\lambda_k(\bar{G})$ and $\lambda_k(G)...
\lambda_k(\bar{G})$ for a graph $G$ of order $n$, as well as for a graph of
order $n$ and size $m$. Some graph classes attaining these bounds are also
given.

12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph