2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65565The infimal Heegaard gradient of a compact 3-manifold was defined and studied by Marc Lackenby in an approach toward the well-known virtually Haken conjecture. As instructive examples, we consider Seifert fibered 3-manifolds, and show that a Seifert fibered 3-manifold has zero infimal Heegaard gradient if and only if it virtually fibers over the circle or over a surface other than the 2-sphere. For a collection of finite coverings of a Seifert fibered 3-manifold, a necessary and sufficient condition to have zero infimal Heegaard gradient is also given.9 pages; revised version; Comments about Heegaard splittings of Seifert fibered 3-manifolds added, proofs in Section 5 revised, and typos correctedGeometric Topology57M10; 57N10; 57M50text