Abstract
Exact algorithms have made a little progress for the 3-coloring problem since 1976: improved from O(1.4422n n O(1)) to O(1.3289n n O(1)). The best exact algorithm for the 3-coloring problem is by Beigel and Eppstein, and its analysis is very complicated. In this paper, we study the parameterized 3-coloring problem: partitioning a 3-colorable graph into a bipartite subgraph and an independent set. Taking the size of the bipartite subgraph as the parameter k, we develop the first parameter algorithm of complexity O *(1.713k). We use measures other than the given parameter k to achieve better analysis on running time. Such a technique of using novel measures may bring new insight into designing faster algorithms for other NP-hard problems.
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Liu, Y., Wang, Q. (2011). On the Partition of 3-Colorable Graphs. In: Wang, W., Zhu, X., Du, DZ. (eds) Combinatorial Optimization and Applications. COCOA 2011. Lecture Notes in Computer Science, vol 6831. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22616-8_34
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DOI: https://doi.org/10.1007/978-3-642-22616-8_34
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