Meunier Conjecture

Abstract

Frédéric Meunier's question about a multicolored Sperner lemma is addressed, leaving the question of connectivity for the color hypergraphs of such a multicolored simplex. Sperner's lemma asserts the existence of a simplex using all the colors for any vertex coloring of a subdivision of a large simplex with appropriate boundary conditions. Meunier's questions generalizes this to the situation of having several such colorings and asserts the existence of a simplex using enough different colors from each coloring.