The complexity of colouring problems on dense graphs
Theoretical Computer Science
Improved algorithms for 3-coloring, 3-edge-coloring, and constraint satisfaction
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Journal of Computer and System Sciences - Special issue on the fourteenth annual IEE conference on computational complexity
Which problems have strongly exponential complexity?
Journal of Computer and System Sciences
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Introduction to Algorithms
Algorithms for k-colouring and finding maximal independent sets
SODA '03 Proceedings of the fourteenth 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
On the Hardness of 4-Coloring a 3-Colorable Graph
SIAM Journal on Discrete Mathematics
Inclusion--Exclusion Algorithms for Counting Set Partitions
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
An O*(2^n ) Algorithm for Graph Coloring and Other Partitioning Problems via Inclusion--Exclusion
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
3-coloring in time O (1.3289n)
Journal of Algorithms
| Hi-index | 0.89 |
We show that the 3-colorability problem can be solved in O(1.296^n) 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 2^o^(^n^) time for graphs having minimum degree at least @w(n) where @w(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 2^o^(^n^) time nor a 2^o^(^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(1.2535^n) time.