Around Sperner's lemma

Abstract

We consider a generalization of the classic Sperner lemma. This lemma states that every Sperner coloring of a triangulation of a simplex contains a fully colored simplex. We found a weaker assumption than Sperner's coloring. It is also shown that the main theorem implies Tucker's lemma and some other theorems.

15 pages, 6 figures. arXiv admin note: text overlap with arXiv:1212.1899

References in corpus (1)

• Kakutani type Borsuk-Ulam theorem