... 1, i, i - 1 with e ≤ i - 1 and i + 1 ≤ n. Proof. The proof is similar to that of Proposition 1. Proposition 3. For n > 3 an optimal tour of Problem B cannot pass through three successive ... vertices of T2 and finally vertices of Tq. The vertices of the same class are numbered in an arbitrary order. 2. Basic properties of optimal tours We now consider the problem of finding ... Conference on Mathematics, Mechanics, and Informatics, Hanoi, 7/10/2006, on the occasion of 50th Anniversary of Department of Mathematics, Mechanics and Informatics, Vietnam National University Hanoi....