Abstract
A polynomial time algorithm for testing isomorphism of graphs which are pairwise k -separable for fixed k is given. The pairwise k -separable graphs are those graphs where each pair of distinct vertices are k -separable. This is a natural generalization of the bounded valence test of Luks. The subgroup of automorphisms of a hypergraph whose restriction to the vertices is in a given Γ k group, for fixed k is constructed in polynomial time.
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