A labeling of the Simplex-Lattice Hypergraph with at most 2 colors on each hyperedge

TL;DR

This paper affirms the existence of a Sperner-admissible labeling for the simplex-lattice hypergraph where each hyperedge contains at most two colors, addressing a question posed by Mirzakhani and Vondrak.

Contribution

It provides a positive solution to the open problem of Sperner-admissible labeling with limited colors per hyperedge in the simplex-lattice hypergraph.

Findings

Existence of Sperner-admissible labeling with at most 2 colors per hyperedge

Addresses an open question by Mirzakhani and Vondrak

Advances understanding of hypergraph colorings and labelings

Abstract

This paper provides a positive answer to the question of Mirzakhani and Vondrak that asks if there is a Sperner-admissible labeling of the simplex-lattice hypergraph such that each hyperedge uses at most 2 colors.