Graphs whose Kronecker covers are bipartite Kneser graphs

Abstract

We show that there are k simple graphs whose Kronecker covers are isomorphic to the bipartite Kneser graph H(n,k), and determine the automorphism groups of these graphs. Using the neighborhood complexes of graphs, we also show that the chromatic numbers of these graphs coincide with χ(K(n,k))=n−2k+2.