2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/99251We present a constructive proof of Ky Fan's combinatorial lemma concerning labellings of triangulated spheres. Our construction works for triangulations of $S^n$ that contain a flag of hemispheres. As a consequence, we produce a constructive proof of Tucker's lemma that holds for a larger class of triangulations than previous constructive proofs.related work at http://www.math.hmc.edu/~su/papers.htmlCombinatoricsAlgebraic TopologyPrimary 55M20; Secondary 05A99, 52B70text