Spectral bounds for the independence number of graphs and even uniform hypergraphs

TL;DR

This paper develops spectral bounds for the independence number of graphs and hypergraphs, extending classical bounds like Hoffman and providing spectral conditions for key graph invariants.

Contribution

It introduces new spectral upper bounds for independence numbers of even uniform hypergraphs and graphs, extending Hoffman and Lovász bounds to broader classes.

Findings

Spectral upper bounds for independence numbers of hypergraphs and graphs.

Extension of Hoffman bound to even uniform hypergraphs.

Spectral conditions for independence number, Shannon capacity, and Lovász number.

Abstract

In this paper, we give spectral upper bounds for the independence number of even uniform hypergraphs and graphs, extend the Hoffman bound to even uniform hypergraphs, and give a simple spectral condition for determining the independence number, the Shannon capacity and the Lov\'{a}sz number of a graph. The Hoffman bound on the Lov\'{a}sz number is also extended from regular graphs to general graphs.