Article - preprint
We present a proof of Ky Fan's combinatorial lemma on labellings of triangulated spheres that differs from earlier proofs in that it is constructive. We slightly generalize the hypotheses of Fan's lemma to allow for triangulations of Sn that contain a flag of hemispheres. As a consequence, we can obtain a constructive proof of Tucker's lemma that holds for a more general class of triangulations than the usual version.
© 2005 Elsevier
Timothy Prescott and Francis Edward Su. A constructive proof of Ky Fan's generalization of Tucker's lemma. J. Combin. Theory Ser. A, 111(2):257–265, 2005.
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Author's pre-print manuscript available for download.
For the publisher's version, please visit http://dx.doi.org/10.1016/j.jcta.2004.12.005.