Lower Bound on the Chromatic Number by Spectra of Weighted Adjacency Matrices

TL;DR

This paper introduces a spectral method to establish lower bounds on a graph's chromatic number using weighted adjacency matrices derived from Hadamard products with Hermitian matrices.

Contribution

It presents a novel spectral approach for bounding the chromatic number based on spectra of weighted adjacency matrices, extending previous methods.

Findings

Provides a new spectral lower bound for chromatic number

Uses Hadamard products with Hermitian matrices for weighting

Enhances understanding of graph coloring via spectral properties

Abstract

A lower bound on the chromatic number of a graph is derived by majorization of spectra of weighted adjacency matrices. These matrices are given by Hadamard products of the adjacency matrix and arbitrary Hermitian matrices.