A Constructive Proof of Tucker's Combinatorial Lemma

摘要

Tucker's combinatorial lemma is concerned with certain labelings of the vertices of a triangulation of the n-ball. It can be used as a basis for the proof of antipodal-point theorems in the same way that Sperner's lemma yields Brouwer's theorem. Here we give a constructive proof, which thereby yields algorithms for antipodal-point problems. The method used is based on an algorithm of Reiser. (Author)