2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/161572We give bounds on the global dimension of a finite length, piecewise hereditary category in terms of quantitative connectivity properties of its graph of indecomposables. We use this to show that the global dimension of a finite dimensional, piecewise hereditary algebra A cannot exceed 3 if A is an incidence algebra of a finite poset or more generally, a sincere algebra. This bound is tight.7 pages; slightly revised; to appear in J. Pure Appl. AlgebraRings and AlgebrasRepresentation Theory18G20; 18E30; 18F20; 16G20; 06A11text