On the first and second eigenvalue of finite and infinite uniform hypergraphs

TL;DR

This paper establishes lower bounds for the first and second eigenvalues of regular, linear uniform hypergraphs, extending classical spectral graph theory results to hypergraph structures.

Contribution

It introduces new lower bounds for eigenvalues in hypergraphs, including a generalization of the Alon-Boppana Theorem to hypergraph settings.

Findings

Derived lower bounds for eigenvalues of hypergraphs

Extended Alon-Boppana Theorem to hypergraphs

Provided spectral properties for regular linear hypergraphs

Abstract

Lower bounds for the first and the second eigenvalue of uniform hypergraphs which are regular and linear are obtained. One of these bounds is a generalization of the Alon-Boppana Theorem to hypergraphs.