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Is it true that for a symmetric TSP instance in the sequence of edges generated by successively:

  • calculating the optimal 2-factor
  • adding cardinality constraints on the edgesets of the 2-factor's connected components

an edge that constituted to the optimal 2-factor of the $i$-th iteration but not to the 2-factor of the $i+1$-st iteration can't reappear in any of the 2-factors of later iterations?

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