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

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

PLOS ONE, 2026, vol. 21, issue 8, 1-15

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.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:plo:pone00:0356507

DOI: 10.1371/journal.pone.0356507

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