The problem of representation of a poligonal domain as a union of the minimum number of convex poligons

Abstract

The problem of partition of a poligonal domain with arbitrary holes into a minimal number of convex parts is solved. It is show that this minimal number equals m+c-h-e, where m, c, h and e are respectively the measure of local nonconvexity, the number of connected components, the number of formal holes, and the effective number of region.