Ordered Vertex Removal and Subgraph Problems Vertex Removal and Graph Problems
نویسنده
چکیده
Several new graph theoretic problems, which arise naturally from existing coloring algorithms, are de ned. The complementary High Degree Vertex Removal Problem and Low Degree Vertex Removal Problem are both shown to be NP-complete. The Low Degree Subgraph Problem is de ned and shown to be NP-complete, whereas, the \complementary" problem for high degree subgraphs was previously shown to be P-complete. Since the obvious sequential algorithms for computing the low degree subgraph and high degree subgraph are based on high degree vertex removal and low degree vertex removal respectively, we nd this is an interesting result. The \greedy" versions of the vertex removal and subgraph problems are shown to be P-complete. In addition, a natural lexicographic version of the Low Degree Subgraph Problem is shown to be NP-complete. 3
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