Longest Hamiltonian in N_{odd-}Gon

ABSTRACT

We single out the polygonal paths
of n_{odd} -1 order that solve each
of the different longest
non-cyclic Euclidean Hamiltonian path problems in networks by an
arithmetic algorithm. As by product, the procedure determines the winding index
of cyclic Hamiltonian polygonals on the vertices of a regular polygon.

Cite this paper

B. Niel, "Longest Hamiltonian in N_{odd-}Gon," *Open Journal of Discrete Mathematics*, Vol. 3 No. 2, 2013, pp. 75-82. doi: 10.4236/ojdm.2013.32015.

B. Niel, "Longest Hamiltonian in N

References

[1] B. I. Niel, “Every Longest Hamiltonian Path in Even N-Gons,” Discrete Mathematics, Algorithms and Applications, Vol. 4, No. 4, 2012, p. 16. doi:10.1142/S1793830912500577

[2] B. I. Niel, “Viajes Sobre Nodd-Gons,” EAE, 2012.

[3] B. I. Niel, W. A. Reartes and N. B. Brignole, “Every Longest Hamiltonian Path in Odd Nodd-Gons,” SIAM Conference on Discrete Mathematics, Austin, 14-17 June 2010, p. 42.

[4] D. Applegate, R. Bixby, V. Chavatal and W. Cook, “Traveling Salesman Problem: A Computational Study,” Princeton University Press, Princeton, 2006.

[5] A. Barvinok, E. K. Gimadi and A. I. Serdyukov, “The Maximum Traveling Salesman Problem,” In: G. Gutin and A. P. Punnen, Eds., The Traveling Salesman Problem and Its Variations, Kluwer Academic Publishers. Dordrecht, 2002.

[6] F. Buckly and F. Harary, “Distance in Graphs,” Addison-Wesley Publishing Co., Boston, 1990.

[7] S. P. Fekete, H. Meijer, A. Rohe and W. Tietze, “Solving a ‘Hard’ Problem to Approximate an ‘Easy’ One: Heuristics for Maximum Matchings and Maximum Traveling Salesman Problems,” Journal of Experimental Algorithms, Vol. 7, 2002, 11 Pages.

[8] A. Kirillov, “On Regular Polygons, Euler’s Function, and Fermat Numbers,” In: S. Tabachnikov, Ed., Kvant Selecta: Algebra and Analysis, Amer Mathematical Society, Providence, 1999, pp. 87-98.

[9] H. S. M. Coxeter, “Introduction to Geometry,” John Wiley & Sons, Inc., Hoboken, 1963.

[10] B. I. Niel, “Geometry of the Euclidean Hamiltonian Sub-optimal and Optimal Paths in the N（k_{K}(n√1)，(d_{ij})）_{nxn}）’s Networks,” Proceedings of the VIII Dr. Antonio A. R. Monteiro, Congress of Mathematics, 26-28 May 2005, Bahía Blanca, pp. 67-84.
http://inmabb.criba.edu.ar/cm/actas/pdf

[11] W. R. Hamilton, “On a General Method of Expressing the Paths of Light, and of the Planets, by the Coefficients of a Characteristic Function,” Vol. I, Dublin University Review and Quarterly Magazine, Dublin, 1833, pp. 795-826.

[12] B. I. Niel, “Hamilton’s Real Find on Geometric Optics in a Hamiltonian Play,” Proceedings of Modelling and Simulation, MS’2004, Lyon, 5-7 July 2004, pp. 9.9-9.13

[1] B. I. Niel, “Every Longest Hamiltonian Path in Even N-Gons,” Discrete Mathematics, Algorithms and Applications, Vol. 4, No. 4, 2012, p. 16. doi:10.1142/S1793830912500577

[2] B. I. Niel, “Viajes Sobre Nodd-Gons,” EAE, 2012.

[3] B. I. Niel, W. A. Reartes and N. B. Brignole, “Every Longest Hamiltonian Path in Odd Nodd-Gons,” SIAM Conference on Discrete Mathematics, Austin, 14-17 June 2010, p. 42.

[4] D. Applegate, R. Bixby, V. Chavatal and W. Cook, “Traveling Salesman Problem: A Computational Study,” Princeton University Press, Princeton, 2006.

[5] A. Barvinok, E. K. Gimadi and A. I. Serdyukov, “The Maximum Traveling Salesman Problem,” In: G. Gutin and A. P. Punnen, Eds., The Traveling Salesman Problem and Its Variations, Kluwer Academic Publishers. Dordrecht, 2002.

[6] F. Buckly and F. Harary, “Distance in Graphs,” Addison-Wesley Publishing Co., Boston, 1990.

[7] S. P. Fekete, H. Meijer, A. Rohe and W. Tietze, “Solving a ‘Hard’ Problem to Approximate an ‘Easy’ One: Heuristics for Maximum Matchings and Maximum Traveling Salesman Problems,” Journal of Experimental Algorithms, Vol. 7, 2002, 11 Pages.

[8] A. Kirillov, “On Regular Polygons, Euler’s Function, and Fermat Numbers,” In: S. Tabachnikov, Ed., Kvant Selecta: Algebra and Analysis, Amer Mathematical Society, Providence, 1999, pp. 87-98.

[9] H. S. M. Coxeter, “Introduction to Geometry,” John Wiley & Sons, Inc., Hoboken, 1963.

[10] B. I. Niel, “Geometry of the Euclidean Hamiltonian Sub-optimal and Optimal Paths in the N（k

[11] W. R. Hamilton, “On a General Method of Expressing the Paths of Light, and of the Planets, by the Coefficients of a Characteristic Function,” Vol. I, Dublin University Review and Quarterly Magazine, Dublin, 1833, pp. 795-826.

[12] B. I. Niel, “Hamilton’s Real Find on Geometric Optics in a Hamiltonian Play,” Proceedings of Modelling and Simulation, MS’2004, Lyon, 5-7 July 2004, pp. 9.9-9.13