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Recently it has been aroused a great interest about explosive (i.e.,discontinuous) transitions. They manifest in distinct systems, such assynchronization in coupled oscillators, percolation regime, absorbing phasetransitions and more recently, in the majority-vote (MV) model with inertia. Inthe latter, the model rules are slightly modified by the inclusion of a termdepending on the local spin (an inertial term). In such case, Chen et al. (PhysRev. E {5}, 042304 (2017)) have found that relevant inertia changes the natureof the phase transition in complex networks, from continuous to discontinuous.Here we give a further step by embedding inertia only in vertices with degreelarger 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 anexplosive transition is presented in both homogeneous and heterogeneousstructures for small and intermediate $k^*$'s. Otherwise, large restriction cansustain a discontinuous transition only in the heterogeneous case. This sharessome similarity with recent results for the Kuramoto model (Phys Rev. E {91},022818 (2015)). Surprisingly, intermediate restriction and large inertia areresponsible for the emergence of an extra phase, in which the system ispartially synchronized and the classification of phase transition depends onthe inertia and the lattice topology. In this case, the system exhibits twophase transitions.

Partial inertia induces additional phase transition in the explosive majority vote model