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For the Traveling Salesman Problem (TSP) on Halin graphs with three types of cost functions: sum, bottleneck and balanced and with arbitrary real edge costs we compute in polynomial time the persistency partition , , of the edge set E, where:
= e ∈ E, e belongs to all optimum solutions,
= e ∈ E, e does not belong to any optimum solution and
= e ∈ E, e belongs to some but not to all optimum solutions.
For each fixed pair α,c > 0 let INDEPENDENT SET () and INDEPENDENT SET () be the problem INDEPENDENT SET restricted to graphs on n vertices with or edges, respectively. Analogously, HAMILTONIAN CIRCUIT () and HAMILTONIAN PATH () are the problems HAMILTONIAN CIRCUIT and HAMILTONIAN PATH restricted to graphs with edges. For each ϵ > 0 let HAMILTONIAN CIRCUIT (m ≥ (1 - ϵ)(ⁿ₂)) and HAMILTONIAN PATH (m ≥ (1 - ϵ)(ⁿ₂)) be the problems HAMILTONIAN CIRCUIT and HAMILTONIAN PATH restricted...
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