| 11. | This means that vertex cover is fixed-parameter tractable with the size of the solution as the parameter.
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| 12. | Vertex cover remains NP-complete even in cubic graphs and even in planar graphs of degree at most 3.
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| 13. | For instance, for the vertex cover problem, the parameter can be the number of vertices in the cover.
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| 14. | On the other hand, the related problem of finding a smallest vertex cover is an NP-hard problem.
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| 15. | Thus we can conclude that if we minimize the sum of y _ v we have also found the minimum vertex cover.
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| 16. | The vertex cover problem is an NP-complete problem : it was one of Karp's 21 NP-complete problems.
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| 17. | K�nig's theorem states that, in bipartite graphs, the maximum matching is equal in size to the minimum vertex cover.
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| 18. | For instance, time bounds of this form are known for finding vertex covers and dominating sets of size " k ".
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| 19. | The complement of " A " forms a vertex cover in " G " with the same cardinality as this matching.
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| 20. | Despite being hard for its natural parameter, boxicity is fixed-parameter tractable when parameterized by the vertex cover number of the input graph.
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