### Abstract

The subject of this paper is the Independent Set problem for bounded node degree graphs. It is shown that the problem remains MAX SNP-complete even when graphs are restricted to being of degree bounded by 3 or to being 3-regular. Some related problems are also shown to be MAX SNP-complete at the lowest possible degree bounds. We next study a better polynomial time approximation of the problem for degree 3 graphs. The performance ratio is improved from the previous best of 5/4 to arbitrarily close to 6/5 for degree 3 graphs and to 7/6 for cubic graphs. When combined with existing techniques this result also leads to approximation ratios, (B + 3)/5 + ε for the independent set problem and 2 - 5/(B + 3) + ε for the vertex cover problem on graphs of degree B, improving previous bounds for relatively small odd B.

Original language | English (US) |
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Pages (from-to) | 115-132 |

Number of pages | 18 |

Journal | Theory of Computing Systems |

Volume | 32 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 1999 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computational Theory and Mathematics

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## Cite this

*Theory of Computing Systems*,

*32*(2), 115-132. https://doi.org/10.1007/s002240000113