Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Unifying Model for Locally Constrained Spanning Tree Problems   Given a graph $G$ and a digraph $D$ whose vertices are the edges of $G$, we
investigate the problem of finding a spanning tree of $G$ that satisfies the
constraints imposed by $D$. The restrictions to add an edge in the tree depend
on its neighborhood in $D$. Here, we generalize previously investigated
problems by also considering as input functions $\ell$ and $u$ on $E(G)$ that
give a lower and an upper bound, respectively, on the number of constraints
that must be satisfied by each edge. The produced feasibility problem is
denoted by \texttt{G-DCST}, while the optimization problem is denoted by
\texttt{G-DCMST}. We show that \texttt{G-DCST} is NP-complete even under strong
assumptions on the structures of $G$ and $D$, as well as on functions $\ell$
and $u$. On the positive side, we prove two polynomial results, one for
\texttt{G-DCST} and another for \texttt{G-DCMST}, and also give a simple
exponential-time algorithm along with a proof that it is asymptotically optimal
under the \ETH. Finally, we prove that other previously studied constrained
spanning tree (\textsc{CST}) problems can be modeled within our framework,
namely, the \textsc{Conflict CST}, the \textsc{Forcing CS, the \textsc{At Least
One/All Dependency CST}, the \textsc{Maximum Degree CST}, the \textsc{Minimum
Degree CST}, and the \textsc{Fixed-Leaves Minimum Degree CST}.

17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
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
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg