Balanced triangulations on few vertices

A classical problem in combinatorial and computational topology asks for the minimum number of vertices needed to triangulate a certain manifold. In this talk I will focus on the family of balanced simplicial complexes, that is d-dimensional complexes whose underlying graph is (d+1)-colorable, and I will exhibit balanced triangulations of surfaces and 3-manifolds on few vertices which are the result of an implementation of local flips preserving the coloring condition.