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

Ognjen Papaz; Duško Jojić

doi:10.48550/arxiv.2511.03036

November 4, 2025Open Access

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

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Key Points

Positive results demonstrate the feasibility of two-color labeling for simplex-lattice hypergraphs, confirming a significant question in the field.
The work shows that a Sperner-admissible labeling is indeed achievable with only two colors on each hyperedge, presenting a notable finding in graph theory.
Analysis was conducted on the coloring properties of hypergraphs focusing on the simplex-lattice structure and its admissibility constraints.
This discovery highlights advances in hypergraph labeling theories, allowing for broader implications in combinatorial mathematics.

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Implication

This analysis reveals a Sperner-admissible labeling with two colors on hyperedges in hypergraphs, implying new insights into graph theory.

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.

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Papaz et al. (2025) studied this question.

synapsesocial.com/papers/690fdcdaf60c54d04ea3806e https://doi.org/10.48550/arxiv.2511.03036

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

Key Points

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Implication

Abstract

Discussion

Cite This Study

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

Key Points

Ask about this paper

Implication

Abstract

Discussion

Cite This Study

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