A direct proof of Shapley-Sperner's lemma based on the KKMS lemma

DOI10.1016/j.jmaa.2020.124789zbMath1494.05098OpenAlexW3106442318WikidataQ124844275 ScholiaQ124844275MaRDI QIDQ1996898

Yanlong Yang, Shunyou Xia, Shu-wen Xiang

Publication date: 28 February 2021

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2020.124789

zbMATH Keywords

Knaster-Kuratowski-Mazurkiewicz-Shapley lemmaShapley-Sperner lemmasimplex subdivisionSperner labeling

Mathematics Subject Classification ID

Graph labelling (graceful graphs, bandwidth, etc.) (05C78)

Cites Work

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• A constructive proof of a permutation-based generalization of Sperner's lemma
• On the Knaster-Kuratowski-Mazurkiewicz-Shapley theorem
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• A simple proof of K-K-M-S theorem
• An elementary proof of the Knaster-Kuratowski-Mazurkiewicz-Shapley theorem
• An extremely simple proof of the K-K-M-S theorem
• An elementary direct proof that the Knaster-Kuratowski-Mazurkiewicz lemma implies Sperner's lemma
• Extensions of two fixed point theorems of F. E. Browder
• The Core of an N Person Game

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