The complexity of colouring problems on dense graphs
Theoretical Computer Science
What are the least tractable instances of max independent set?
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
A general method to speed up fixed-parameter-tractable algorithms
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
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
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
Parameterized complexity: the main ideas and connections to practical computing
Experimental algorithmics
Exact algorithms for NP-hard problems: a survey
Combinatorial optimization - Eureka, you shrink!
Quasiconvex analysis of backtracking algorithms
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Vertex Colouring and Forbidden Subgraphs – A Survey
Graphs and Combinatorics
Spanning trees with many leaves
Journal of Graph Theory
An O(v|v| c |E|) algoithm for finding maximum matching in general graphs
SFCS '80 Proceedings of the 21st Annual Symposium on Foundations of Computer Science
Exact (exponential) algorithms for the dominating set problem
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
Parameterized Complexity
Exact algorithms for dominating set
Discrete Applied Mathematics
Capacitated domination faster than O(2n)
Information Processing Letters
Capacitated domination faster than O(2n)
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
Computing the differential of a graph: Hardness, approximability and exact algorithms
Discrete Applied Mathematics
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We design fast exponential time algorithms for some intractable graph-theoretic problems. Our main result states that a minimum optional dominating set in a graph of order n can be found in time O^*(1.8899^n). Our methods to obtain this result involve matching techniques. The list of the considered problems includes Minimum Maximal Matching, 3-Colourability, Minimum Dominating Edge Set, Minimum Connected Dominating Set (~Maximum Leaf Spanning Tree), Minimum Independent Dominating Set and Minimum Dominating set.