Mathematical Programming

, Volume 26, Issue 3, pp 287–294

Halin graphs and the travelling salesman problem

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

DOI: 10.1007/BF02591867

Cite this article as:
Cornuéjols, G., Naddef, D. & Pulleyblank, W.R. Mathematical Programming (1983) 26: 287. doi:10.1007/BF02591867


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 

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
  5. 5.Centre for Operations Research, and EconometricsLouvain-laneuveBelgium

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