Zero knowledge and the chromatic number
Journal of Computer and System Sciences - Eleventh annual conference on structure and complexity 1996
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
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
Pathwidth of cubic graphs and exact algorithms
Information Processing Letters
3-coloring in time O (1.3289n)
Journal of Algorithms
Better inapproximability results for maxclique, chromatic number and min-3lin-deletion
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Enumerating maximal independent sets with applications to graph colouring
Operations Research Letters
Colorings with few colors: counting, enumeration and combinatorial bounds
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
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We introduce a generic algorithmic technique and apply it on decision and counting versions of graph coloring. Our approach is based on the following idea: either a graph has nice (from the algorithmic point of view) properties which allow a simple recursive procedure to find the solution fast, or the pathwidth of the graph is small, which in turn can be used to find the solution by dynamic programming. By making use of this technique we obtain the fastest known exact algorithms - running in time O(1.7272n) for deciding if a graph is 4-colorable and - running in time O(1.6262n) and O(1.9464n) for counting the number of k-colorings for k = 3 and 4 respectively.