The Existence of Two Mutually Independent Hamiltonian Cycles in Hypercube-Like Graphs

Abstract

The problem of whether or not there are mutually independent hamiltonian cycles in interconnection networks has attracted a great attention in recent years. In this paper, we will show that most of n-dimensional hypercube-like graphs have two mutually independent hamiltonian cycles. Moreover, we also develop a systematic linear time algorithm for constructing two mutually independent hamiltonian cycles in the n-dimensional hypercube Q <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> , n > 3.