On the hardness of approximating minimization problems
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
An Õ(n3/14)-coloring algorithm for 3-colorable graphs
Information Processing Letters
Improved algorithms for 3-coloring, 3-edge-coloring, and constraint satisfaction
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
(H, C, K)-Coloring: Fast, Easy, and Hard Cases
MFCS '01 Proceedings of the 26th International Symposium on Mathematical Foundations of Computer Science
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
Register allocation & spilling via graph coloring
SIGPLAN '82 Proceedings of the 1982 SIGPLAN symposium on Compiler construction
Set Partitioning via Inclusion-Exclusion
SIAM Journal on Computing
3-coloring in time O (1.3289n)
Journal of Algorithms
Finding odd cycle transversals
Operations Research Letters
Enumerating maximal independent sets with applications to graph colouring
Operations Research Letters
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Exact algorithms havemade a little progress for the 3-coloring problem since 1976: improved from O(1.4422nnO(1)) to O(1.3289nnO(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.