A convex n-vertex polygon is partitioned into triangles by nonintersecting diagonals . The following operation, called perestroyka (=reconstruction) , is allowed: two triangles ABD and BCD with a common side may be replaced by the triangles ABC and ACD. By P(n) denote the smallest number of perestroykas needed to transform any partitioning into any other one. Prove that
(a) P(n)≥n−3
(b) P(n)≤2n−7
(c) P(n)≤2n−10 if n≥13 . ( D.Fomin , based on ideas of W. Thurston , D . Sleator, R. Tarjan) combinatoricscombinatorial geometry