Path Separation by Short Cycles.

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. (C) 2016 Wiley Periodicals, Inc.