  Recently it has been aroused a great interest about explosive (i.e.,
discontinuous) transitions. They manifest in distinct systems, such as
synchronization in coupled oscillators, percolation regime, absorbing phase
transitions and more recently, in the majority-vote (MV) model with inertia. In
the latter, the model rules are slightly modified by the inclusion of a term
depending on the local spin (an inertial term). In such case, Chen et al. (Phys
Rev. E {5}, 042304 (2017)) have found that relevant inertia changes the nature
of the phase transition in complex networks, from continuous to discontinuous.
Here we give a further step by embedding inertia only in vertices with degree
larger than a threshold value $\langle k \rangle k^*$, $\langle k \rangle$
being the mean system degree and $k^*$ the fraction restriction. Our results,
from mean-field analysis and extensive numerical simulations, reveal that an
explosive transition is presented in both homogeneous and heterogeneous
structures for small and intermediate $k^*$'s. Otherwise, large restriction can
sustain a discontinuous transition only in the heterogeneous case. This shares
some similarity with recent results for the Kuramoto model (Phys Rev. E {91},
022818 (2015)). Surprisingly, intermediate restriction and large inertia are
responsible for the emergence of an extra phase, in which the system is
partially synchronized and the classification of phase transition depends on
the inertia and the lattice topology. In this case, the system exhibits two
phase transitions.
