On the minimum number of non-monochromatic simplices for Sperner labelings of a regular triangulation.

Authors

Luis Ángel Calvo Pascual, Susana Merchán Rubira, Dulcinea Raboso Paniagua, Javier Rodrigo Hitos, José Samuel Rodríguez García

Published in

PloS one. Volume 21. Issue 8. Pages e0356507. Epub Aug 28, 2026.

Abstract

Motivated by an open problem in the literature stated by Mirzakhani and Vondrák, we give a lower bound of the number of non-monochromatic simplices for Sperner labelings of the vertices of a triangulation of a given k-simplex with vertices of integer coordinates. This triangulation maximizes the number of simplices over all the triangulations of the k-simplex with vertices of integer coordinates.

PMID:
42664290
Bibliographic data and abstract were imported from PubMed on 29 Aug 2026.

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