Tohoku Mathematical Journal
2023
March
SECOND SERIES VOL. 75, NO. 1

Tohoku Math. J.
75 (2023), 119-130

Title CHENG'S MAXIMAL DIAMETER THEOREM FOR HYPERGRAPHS

Author Yu Kitabeppu and Erina Matsumoto

(Received May 17, 2021, revised December 2, 2021)
Abstract. We prove that Cheng's maximal diameter theorem for hypergraphs with positive coarse Ricci curvature. Coarse Ricci curvature on hypergraphs is defined by using the resolvent of the nonlinear Laplacian. As a byproduct of the main theorem, the first non-zero eigenvalue on a hypergraph coincides with the lower bound of the curvature if the hypergraph has the maximal diameter.

Mathematics Subject Classification. Primary 51F99; Secondary 52C99.
Key words and phrases. Hypergraph, coarse Ricci curvature.

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