On the b-chromatic number of Kneser Graphs

TL;DR

This paper proves that the b-chromatic number of Kneser graphs $KG(m,n)$ is at least twice the binomial coefficient of half of m choose n, confirming a previous conjecture.

Contribution

It establishes a lower bound for the b-chromatic number of Kneser graphs, resolving a conjecture in the field.

Findings

b-chromatic number of $KG(m,n)$ is ≥ 2 * $inom{loor{m/2}}{n}$

Confirmed a conjecture regarding the b-chromatic number of Kneser graphs

Provides a new lower bound for the b-chromatic number

Abstract

In this note, we prove that for any integer $n\geq 3$ the b-chromatic number of the Kneser graph $KG(m,n)$ is greater than or equal to $2{\lfloor {m\over 2} \rfloor \choose n}$. This gives an affirmative answer to a conjecture of [6].