Halin graphs and the travelling salesman problem
- Cite this article as:
- Cornuéjols, G., Naddef, D. & Pulleyblank, W.R. Mathematical Programming (1983) 26: 287. doi:10.1007/BF02591867
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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.