Abstract
We show that the k-Vertex Cover problem in degree-3 graphs can be solved in O *(1.1616k) time, which improves previous results of O *(1.1940k) by Chen, Kanj and Xia and O *(1.1864k) by Razgon. In this paper, we will present a new way to analyze algorithms for the problem. We use \(r=k-\frac{2}{5}n\) to measure the size of the search tree, and then get a simple \(O(1.6651^{k-\frac{2}{5}n_0})\)-time algorithm, where n 0 is the number of vertices with degree ≥ 2 in the graph. Combining this result with fast algorithms for the Maximum Independent Set problem in degree-3 graphs, we improve the upper bound for the k-Vertex Cover problem in degree-3 graphs.
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Xiao, M. (2010). A Note on Vertex Cover in Graphs with Maximum Degree 3. In: Thai, M.T., Sahni, S. (eds) Computing and Combinatorics. COCOON 2010. Lecture Notes in Computer Science, vol 6196. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14031-0_18
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DOI: https://doi.org/10.1007/978-3-642-14031-0_18
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