A topological proof of Chen's alternative Kneser coloring theorem

Abstract

Johnson, Holroyd and Stahl [5] conjectured that the circular chromatic number of the Kneser graph is equal to the ordinary chromatic number. Chen completely confirmed the conjecture in [4]. Chen's alternative Kneser coloring theorem is a key lemma in his proof of Johnson-Holroyd-Stahl conjecture. Chen [4] and Chang, Liu and Zhu [3] proved the theorem by using Fan's lemma. In this paper, we prove Chen's alternative Kneser coloring theorem by using cohomology.