Hamiltonian cycles and paths with a prescribed set of edges in hypercubes and dense sets

Abstract

This paper studies techniques of finding hamiltonian paths and cycles in hypercubes and dense sets of hypercubes. This problem is, in general, easily solvable but here the problem was modified by the requirement that a set of edges has to be used in such path or cycle. The main result of this paper says that for a given n, any sufficiently large hypercube contains a hamiltonian path or cycle with prescribed n edges just when the family of the edges satisfies certain natural necessary conditions. Analogous results are presented for dense sets. © 2005 Wiley Periodicals, Inc. J Graph Theory