A Constructive Proof of Ky Fan's Generalization of Tucker's Lemma

We 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.