The 3-Opt procedure deals with interchanging three edges of a tour with three edges not on that tour. For n≥6, the 3-Interchange Graph is a graph on 1/2(n-1)! vertices, corresponding to the hamiltonian tours in K_n; two vertices are adjacent iff the corresponding hamiltonian tours differ in an interchange of 3 edges; i.e. the tours differ in a single 3-Opt step. It is shown that the 3-Interchange Graph is a hamiltonian subgraph of the Symmetric Traveling Salesman Polytope. Upper bounds are derived for the diameters of the 3-Interchange Graph and the union of the 2- and the 3-Interchange Graphs. Finally, some new adjacency properties for the Asymmetric Traveling Salesman Polytope and the Assignment Polytope are given.
@article{bwmeta1.element.bwnjournal-article-zmv22z3p351bwm,
author = {Gerard Sierksma},
title = {Hamiltonicity and the 3-Opt procedure for the traveling Salesman problem},
journal = {Applicationes Mathematicae},
volume = {22},
year = {1994},
pages = {351-358},
zbl = {0818.90126},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-zmv22z3p351bwm}
}
Sierksma, Gerard. Hamiltonicity and the 3-Opt procedure for the traveling Salesman problem. Applicationes Mathematicae, Tome 22 (1994) pp. 351-358. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-zmv22z3p351bwm/
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