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- Hamiltonian_completion abstract "The Hamiltonian completion problem is to find the minimal number of edges to add to a graph to make it Hamiltonian.The problem is clearly NP-hard in general case (since its solution gives an answer to the NP-complete problem of determining whether a given graph has a Hamiltonian cycle). The associated decision problem of determining whether K edges can be added to a given graph to produce a Hamiltonian graph is NP-complete.Moreover, Hamiltonian completion belongs to the APX complexity class, i.e., it is unlikely that efficient constant ratio approximation algorithms exist for this problem.The problem may be solved in polynomial time for certain classes of graphs, including series-parallel graphs and their generalizations, which include outerplanar graphs, as well as for a line graph of a treeor a cactus graph.Gamarnik et al. use a linear time algorithm for solving the problem on trees to study the asymptotic number of edges that must be added for sparse random graphs to make them Hamiltonian.".
- Hamiltonian_completion wikiPageID "9944425".
- Hamiltonian_completion wikiPageLength "3121".
- Hamiltonian_completion wikiPageOutDegree "17".
- Hamiltonian_completion wikiPageRevisionID "652698035".
- Hamiltonian_completion wikiPageWikiLink APX.
- Hamiltonian_completion wikiPageWikiLink Cactus_graph.
- Hamiltonian_completion wikiPageWikiLink Category:Hamiltonian_paths_and_cycles.
- Hamiltonian_completion wikiPageWikiLink Category:NP-complete_problems.
- Hamiltonian_completion wikiPageWikiLink Complexity_class.
- Hamiltonian_completion wikiPageWikiLink Constant_ratio_approximation.
- Hamiltonian_completion wikiPageWikiLink Decision_problem.
- Hamiltonian_completion wikiPageWikiLink Graph_(mathematics).
- Hamiltonian_completion wikiPageWikiLink Hamiltonian_cycle.
- Hamiltonian_completion wikiPageWikiLink Hamiltonian_graph.
- Hamiltonian_completion wikiPageWikiLink Hamiltonian_path.
- Hamiltonian_completion wikiPageWikiLink Line_graph.
- Hamiltonian_completion wikiPageWikiLink NP-complete.
- Hamiltonian_completion wikiPageWikiLink NP-completeness.
- Hamiltonian_completion wikiPageWikiLink NP-hard.
- Hamiltonian_completion wikiPageWikiLink NP-hardness.
- Hamiltonian_completion wikiPageWikiLink Outerplanar_graph.
- Hamiltonian_completion wikiPageWikiLink Polynomial_time.
- Hamiltonian_completion wikiPageWikiLink Random_graph.
- Hamiltonian_completion wikiPageWikiLink Series-parallel_graph.
- Hamiltonian_completion wikiPageWikiLink Time_complexity.
- Hamiltonian_completion wikiPageWikiLinkText "Hamiltonian completion".
- Hamiltonian_completion hasPhotoCollection Hamiltonian_completion.
- Hamiltonian_completion subject Category:Hamiltonian_paths_and_cycles.
- Hamiltonian_completion subject Category:NP-complete_problems.
- Hamiltonian_completion type Object.
- Hamiltonian_completion comment "The Hamiltonian completion problem is to find the minimal number of edges to add to a graph to make it Hamiltonian.The problem is clearly NP-hard in general case (since its solution gives an answer to the NP-complete problem of determining whether a given graph has a Hamiltonian cycle).".
- Hamiltonian_completion label "Hamiltonian completion".
- Hamiltonian_completion sameAs m.02pxqn7.
- Hamiltonian_completion sameAs Q5645290.
- Hamiltonian_completion sameAs Q5645290.
- Hamiltonian_completion wasDerivedFrom Hamiltonian_completion?oldid=652698035.
- Hamiltonian_completion isPrimaryTopicOf Hamiltonian_completion.