Date: 01 Jun 2005

On approximation properties of the Independent set problem for degree 3 graphs

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The main problem we consider in this paper is the Independent Set problem for bounded degree graphs. It is shown that the problem remains MAX SNP-complete when the maximum degree is bounded by 3. Some related problems are also shown to be MAX SNP-complete at the lowest possible degree bounds. Next we study better poly-time approximation of the problem for degree 3 graphs, and improve the previously best ratio, 5/4, to arbitrarily close to 6/5. This result also provides improved poly-time approximation ratios, B+3/5+ε, for odd degree B.