  The Angular Constrained Minimum Spanning Tree Problem ($\alpha$-MSTP) is
defined in terms of a complete undirected graph $G=(V,E)$ and an angle $\alpha
\in (0,2\pi]$. Vertices of $G$ define points in the Euclidean plane while
edges, the line segments connecting them, are weighted by the Euclidean
distance between their endpoints. A spanning tree is an $\alpha$-spanning tree
($\alpha$-ST) of $G$ if, for any $i \in V$, the smallest angle that encloses
all line segments corresponding to its $i$-incident edges does not exceed
$\alpha$. $\alpha$-MSTP consists in finding an $\alpha$-ST with the least
weight. We introduce two $\alpha-$MSTP integer programming formulations,
${\mathcal F}_{xy}^*$ and $\mathcal{F}_x^{++}$ and their accompanying
Branch-and-cut (BC) algorithms, BCFXY$^*$ and BCFX$^{++}$. Both formulations
can be seen as improvements over formulations coming from the literature. The
strongest of them, $\mathcal{F}_x^{++}$, was obtained by: (i) lifting an
existing set of inequalities in charge of enforcing $\alpha$ angular
constraints and (ii) characterizing $\alpha$-MSTP valid inequalities from the
Stable Set polytope, a structure behind $\alpha-$STs, that we disclosed here.
These formulations and their predecessors in the literature were compared from
a polyhedral perspective. From a numerical standpoint, we observed that
BCFXY$^*$ and BCFX$^{++}$ compare favorably to their competitors in the
literature. In fact, thanks to the quality of the bounds provided by
$\mathcal{F}_x^{++}$, BCFX$^{++}$ seems to outperform the other existing
$\alpha-$MSTP algorithms. It is able to solve more instances to proven
optimality and to provide sharper lower bounds, when optimality is not attested
within an imposed time limit. As a by-product, BCFX$^{++}$ provided 8 new
optimality certificates for instances coming from the literature.
