Mutually Independent Hamiltonian Cycles
نویسندگان
چکیده
A Hamiltonian cycle of a graph G is a cycle which contains all vertices of G. Two Hamiltonian cycles C1 = 〈u0, u1, u2, ..., un−1, u0〉 and C2 = 〈v0, v1, v2, ..., vn−1, v0〉 in G are independent if u0 = v0, ui 6= vi for all 1 ≤ i ≤ n − 1. If any two Hamiltonian cycles of a Hamiltonian cycles set C = {C1, C2, ..., Ck} are independent, we call C is mutually independent. The mutually independent Hamiltonicity IHC(G) = k means there exists a maximum integer k such that there exists k-mutually independent Hamiltonian cycles start from any vertex of G. In this paper, we prove that IHC(Cm × Cn) = 4, for m,n ≥ 3, m,n are odd.
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تاریخ انتشار 2012