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• W1986075609 abstract "We show that the 3-colorability problem can be solved in O(1.296n) time on any n-vertex graph with minimum degree at least 15. This algorithm is obtained by constructing a dominating set of the graph greedily, enumerating all possible 3-colorings of the dominating set, and then solving the resulting 2-list coloring instances in polynomial time. We also show that a 3-coloring can be obtained in 2o(n) time for graphs having minimum degree at least ω(n) where ω(n) is any function which goes to ∞. We also show that if the lower bound on minimum degree is replaced by a constant (however large it may be), then neither a 2o(n) time nor a 2o(m) time algorithm is possible (m denotes the number of edges) for 3-colorability unless Exponential Time Hypothesis (ETH) fails. We also describe an algorithm which obtains a 4-coloring of a 3-colorable graph in O(1.2535n) time." @default.
• W1986075609 created "2016-06-24" @default.
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• W1986075609 date "2011-02-01" @default.
• W1986075609 modified "2023-09-27" @default.
• W1986075609 title "Dominating set based exact algorithms for 3-coloring" @default.
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• W1986075609 doi "https://doi.org/10.1016/j.ipl.2010.11.009" @default.
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