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 (2)

• Kakutani type Borsuk-Ulam theorem
• Extensions of Sperner and Tucker's lemma for manifolds

Cited by in corpus (7)

• Fairly Dividing a Cake after Some Parts Were Burnt in the Oven
• Sperner type lemma for quadrangulations
• Borsuk - Ulam Type spaces
• Generalizations of Tucker-Fan-Shashkin lemmas
• Fair division and generalizations of Sperner- and KKM-type results
• Homotopy groups and quantitative Sperner-type lemma
• A Proof of Atanassov's Conjecture and Other Generalizations of Sperner's Lemma