We solve two related extremal problems in the theory of permutations. A set Q of permutations of the integers 1 to n is inversion-complete (resp., pair-complete) if for every
Two Hamilton paths in Kn are separated by a cycle of length k if their union contains such a cycle. For K = 4 we bound the asymptotics of the maximum cardinality of a family of Hamilton paths in Kn such that any pair of paths in the family is separated by a cycle of length k. We also deal with related problems, including directed Hamilton paths. © 2016 Wiley Periodicals, Inc.
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