Graphs whose Kronecker covers are bipartite Kneser graphs

TL;DR

This paper identifies specific simple graphs whose Kronecker covers are bipartite Kneser graphs, and determines their chromatic numbers and automorphism groups, advancing understanding of graph coverings and symmetries.

Contribution

It constructs graphs with Kronecker covers isomorphic to bipartite Kneser graphs and computes their chromatic numbers and automorphism groups, revealing new structural insights.

Findings

Existence of k simple graphs with Kronecker cover isomorphic to bipartite Kneser graph

Chromatic numbers of these graphs match n - 2k + 2

Automorphism groups of these graphs are determined

Abstract

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.