Abstract
Given a graph G=(V,E), the Hamiltonian completion number of G, HCN(G), is the minimum number of edges to be added to G to make it Hamiltonian. This problem is known to be \(\mathcal{NP}\) -hard even when G is a line graph. In this paper, local search algorithms for finding HCN(G) when G is a line graph are proposed. The adopted approach is mainly based on finding a set of edge-disjoint trails that dominates all the edges of the root graph of G. Extensive computational experiments conducted on a wide set of instances allow to point out the behavior of the proposed algorithms with respect to both the quality of the solutions and the computation time.
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Detti, P., Meloni, C. & Pranzo, M. Local search algorithms for finding the Hamiltonian completion number of line graphs. Ann Oper Res 156, 5–24 (2007). https://doi.org/10.1007/s10479-007-0231-z
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DOI: https://doi.org/10.1007/s10479-007-0231-z