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The Birkhoff polytope graph has a vertex set equal to the elements of thesymmetric group of degree $n$, and two elements are adjacent if one elementequals the product of the other element with a cycle. Maximal and maximumcliques (sets of pairwise adjacent elements) and independent sets (sets ofpairwise nonadjacent elements) of the Birkhoff polytope graph are studied.Bounds are obtained for different sizes of such sets.

Cliques and independent sets of the Birkhoff polytope graph