# A relative bound for independence

## TL;DR

This paper introduces a new upper bound for a graph's independence number, refining existing bounds by relating it to the Laplacian eigenvalue and specific subgraphs.

## Contribution

It provides a novel, tighter bound on the independence number using spectral graph theory and subgraph analysis.

## Key findings

- The bound improves upon traditional Hoffman-type bounds.
- The bound applies to a wide class of graphs.
- The method links eigenvalues to combinatorial properties.

## Abstract

We prove an upper bound for the independence number of a graph in terms of the largest Laplacian eigenvalue, and of a certain induced subgraph. Our bound is a refinement of a well-known Hoffman-type bound.