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The domino inequalities: facets for the symmetric traveling salesman polytope

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Abstract.

Adam Letchford defines in [4] the Domino Parity inequalities for the Symmetric Traveling Salesman Polytope (STSP) and gives a polynomial algorithm for the separation of such constraints when the support graph is planar, generalizing a result of Fleischer and Tardos [2] for maximally violated comb inequalities. Naddef in [5] gives a set of necessary conditions for such inequalities to be facet defining for the STSP. These conditions lead to the Domino inequalities and it is shown in [5] that one does not lose any facet inducing inequality restricting the Domino Parity inequalities to Domino inequalities, except maybe for some very particular case. We prove here that all the domino inequalities are facet inducing for the STSP, settling the conjecture given in [5]. As a by product we will also have a complete proof that the comb inequalities are facet inducing.

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References

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Authors and Affiliations

  1. Laboratoire d'Informatique et Distribution-IMAG, Institut National Polytechnique de Grenoble

    Denis Naddef & Emmanuel Wild

Authors
  1. Denis Naddef
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  2. Emmanuel Wild
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Correspondence to Denis Naddef.

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Mathematics Subject Classification (2000): Main 90C57, secondary 90C27

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Naddef, D., Wild, E. The domino inequalities: facets for the symmetric traveling salesman polytope. Math. Program., Ser. B 98, 223–251 (2003). https://doi.org/10.1007/s10107-003-0403-9

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  • DOI: https://doi.org/10.1007/s10107-003-0403-9

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