A unifying model for locally constrained spanning tree problems

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