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|Type:||Artigo de periódico|
|Title:||Nonplanar Vertex Deletion: Maximum Degree Thresholds For Np/max Snp-hardness And A Frac(3, 4)-approximation For Finding Maximum Planar Induced Subgraphs|
Herrera de Figueiredo C.M.
|Abstract:||The non planar vertex deletion v d (G), of a graph G is the smallest positive integer k, such that the removal of k vertices from G produces a planar graph. We solve a problem proposed by Yannakakis: find the threshold for the maximum degree of a graph G such that, given a graph G and a positive integer k, to decide whether v d (G) ≤ k is NP-complete. We prove that it is NP-complete to decide whether a maximum degree 3 graph G and a positive integer k satisfy v d (G) ≤ k. We prove that to compute v d (G) is Max SNP-hard when restricted to a cubic input G. We exhibit a polynomial frac(3, 4)-approximation algorithm for finding a maximum planar induced subgraph of a maximum degree 3 graph. © 2004.|
|Appears in Collections:||Unicamp - Artigos e Outros Documentos|
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