A note on vertex cover in graphs with maximum degree 3

Authors:
Mingyu Xiao
Affiliations:
School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, China
Venue:
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
Year:
2010

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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 - 2/5n to measure the size of the search tree, and then get a simple O(1.6651k-2/5n0)-time algorithm, where n0 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.