  We solve three enumerative problems concerning families of planar maps. More
precisely, we establish algebraic equations for the generating function of
non-separable triangulations in which all vertices have degree at least d, for
a certain value d chosen in {3, 4, 5}. The originality of the problem lies in
the fact that degree restrictions are placed both on vertices and faces. Our
proofs first follow Tutte's classical approach: we decompose maps by deleting
the root and translate the decomposition into an equation satisfied by the
generating function of the maps under consideration. Then we proceed to solve
the equation obtained using a recent technique that extends the so-called
quadratic method.
