[@Schechter:1980gr] that can be identified with the “atmospheric scale”. Realistic values for the “solar” mass scale could arise, for example, from adding a scotogenic “dark” sector [@Rojas:2018wym].

Turning to the case n$\geq$3 we have interesting schemes for n=3, that corresponds to the canonical type-I seesaw mechanism [@Valle:2015pba]. The cases n=6, 4 and 2 also provide the setting for “low-scale” seesaw mechanisms in which “quasi”-Dirac heavy neutrinos act as neutrino mass generation messengers. Their masses can be much lower than in the “high-scale” seesaw, possibly at the TeV scale, as neutrino masses are “protected” in ’t-Hooft’s sense. For n=6 we have the template for the sequential “low-scale” seesaw mechanisms, both of the inverse [@Mohapatra:1986bd; @GonzalezGarcia:1988rw] and linear seesaw type [@Akhmedov:1995ip; @Akhmedov:1995vm; @Malinsky:2005bi]. The cases n=4 and n=2 correspond to more economical constructions analogous to n=2,1 of the high-scale seesaw.

In this paper we will be mostly concerned with the effects of sizable Yukawa couplings in the context of high-scale seesaw constructions and their significant impact on the stability of the Higgs vacuum. Here we have studied the effect of such large Yukawa couplings $Y_{\nu}$ on the stability of the electroweak vacuum.

Higgs Vacuum Stability in High-scale Type-I Seesaw {#sec:result-seesaw}
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For 