A new coloring theorem of Kneser graphs

In 1997, Johnson, Holroyd and Stahl conjectured that the circular chromatic number of the Kneser graphs KG ( n , k ) is equal to the chromatic number of these graphs. This was proved by Simonyi and Tardos (2006) [13] and independently by Meunier (2005) [10], if χ ( KG ( n , k ) ) is even. In this paper, we propose an alternative version of Kneserʹs coloring theorem to confirm the Johnson–Holroyd–Stahl conjecture.