Choice number of Kneser graphs

TL;DR

This paper establishes that for certain ranges of parameters, the choice number of Kneser graphs grows proportionally to n log n, providing new bounds for these combinatorial structures.

Contribution

It proves that for k less than n^{0.5 - epsilon}, the choice number of Kneser graphs is Theta(n log n), offering new asymptotic bounds.

Findings

Choice number of Kneser graphs is Theta(n log n) for specified k ranges.

Provides asymptotic bounds for the choice number in new parameter regimes.

Abstract

In this short note, we show that for any $\epsilon >0$ and $k<n^{0.5-\epsilon}$ the choice number of the Kneser graph $KG_{n,k}$ is $\Theta (n\log n)$.