Abstract
A Hamiltonian cycle C of G is described as to emphasize the order of nodes in C. Thus, u/sub 1/ is the beginning node and u/sub i/ is the i-th node in C. Two Hamiltonian cycles of G beginning at u, C/sub 1/= and C/sub 2/= , are independent if u=v/sub 1/=u/sub 1/, and v/sub i//spl ne/u/sub i/ for 1<i/spl les/n(G). A set of Hamiltonian cycles {C/sub 1/, C/sub 2/, ..., C/sub k/} of G are mutually independent if any two different Hamiltonian cycles are independent. The mutually independent Hamiltonianicity of graph G, IHC(G), is the maximum integer k such that for any node u of G there exist k-mutually independent Hamiltonian cycles of G starting at u. Let Q/sub n/ be the n-dimensional hypercube. We prove that IHC(Q/sub n/)=n-1 if n/spl isin/{1, 2, 3} and IHC(Q/sub n/)=n if n/spl ges/4.
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