We show that there are $k$ simple graphs whose Kronecker covers are isomorphic to the bipartite Kneser graph $H(n,k)$, and that their chromatic numbers coincide with $\chi(K(n,k)) = n - 2k + 2$. We also determine the automorphism groups of these graphs.

中文翻译：

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Kronecker 覆盖的图是二部 Kneser 图

我们证明存在 $k$ 个简单图，其 Kronecker 覆盖与二部 Kneser 图 $H(n,k)$ 同构，并且它们的色数与 $\chi(K(n,k)) = n - 2k + 2$。我们还确定了这些图的自同构群。