Johnson, Holroyd and Stahl  conjectured that the circular chromatic number of the Kneser graph is equal to the ordinary chromatic number. Chen completely confirmed the conjecture in . Chen's alternative Kneser coloring theorem is a key lemma in his proof of Johnson-Holroyd-Stahl conjecture. Chen  and Chang, Liu and Zhu  proved the theorem by using Fan's lemma. In this paper, we prove Chen's alternative Kneser coloring theorem by using cohomology.
"A topological proof of Chen's alternative Kneser coloring theorem." Tsukuba J. Math. 42 (2) 251 - 258, December 2018. https://doi.org/10.21099/tkbjm/1554170424