Improved algorithms for 3-coloring, 3-edge-coloring, and constraint satisfaction
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Deciding 3-Colourability in Less Than O(1.415^n) Steps
WG '93 Proceedings of the 19th International Workshop on Graph-Theoretic Concepts in Computer Science
3-coloring in time 0(1.3446^n): a no-MIS algorithm
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Journal of Algorithms
Exact (exponential) algorithms for the dominating set problem
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
Linear kernels in linear time, or how to save k colors in O(n2) steps
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
Improved exponential-time algorithms for treewidth and minimum fill-in
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
Minimizing area and power of sequential CMOS circuits using threshold decomposition
Proceedings of the International Conference on Computer-Aided Design
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We show that, for any n-vertex graph G and integer parameter k, there are at most 34k-n4n-3k maximal independent sets I ⊂ G with |I| ≤ k, and that all such sets can be listed in time O(34k-n4n-3k). These bounds are tight when n/4 ≤ k ≤ n/3. As a consequence, we show how to compute the exact chromatic number of a graph in time O((4/3 + 34/3/4)n) ≅ 2.4150n, improving a previous O((1 + 31/3)n) ≅ 2.4422n algorithm of Lawler (1976).