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Mathematical Programming

, Volume 26, Issue 3, pp 287–294 | Cite as

Halin graphs and the travelling salesman problem

  • G. Cornuéjols
  • D. Naddef
  • W. R. Pulleyblank
Article

Abstract

A Halin graphH=T∪C is obtained by embedding a treeT having no nodes of degree 2 in the plane, and then adding a cycleC to join the leaves ofT in such a way that the resulting graph is planar. These graphs are edge minimal 3-connected, hamiltonian, and in general have large numbers of hamilton cycles. We show that for arbitrary real edge costs the travelling salesman problem can be polynomially solved for such a graph, and we give an explicit linear description of the travelling salesman polytope (the convex hull of the incidence vectors of the hamilton cycles) for such a graph.

Key words

Travelling Salesman Problem Polynomial Algorithm Integer Polytope Polyhedral Combinatorics Halin Graph Roofless Polyhedron Edge Cutset 

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References

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Copyright information

© The Mathematical Programming Society, Inc. 1983

Authors and Affiliations

  • G. Cornuéjols
    • 1
  • D. Naddef
    • 2
  • W. R. Pulleyblank
    • 3
    • 4
  1. 1.Graduate School of Industrial AdministrationCarnegie-Mellon UniversityPittsburghUSA
  2. 2.I.M.A.G.Université Scientifique et Médicale de GrenobleGrenobleFrance
  3. 3.Department of Combinatorics and OptimizationUniversity of WaterlooWaterlooCanada
  4. 4.Institut für Operations ResearchUniversität BonnFederal Republic of Germany

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