The Jordan-Scho¨nflies theorem and the classification of surfaces
American Mathematical Monthly
Handbook of combinatorics (vol. 1)
Refined Search Tree Technique for DOMINATING SET on Planar Graphs
MFCS '01 Proceedings of the 26th International Symposium on Mathematical Foundations of Computer Science
Fixed Parameter Algorithms for PLANAR DOMINATING SET and Related Problems
SWAT '00 Proceedings of the 7th Scandinavian Workshop on Algorithm Theory
Efficient Data Reduction for DOMINATING SET: A Linear Problem Kernel for the Planar Case
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
Parameterized Complexity: Exponential Speed-Up for Planar Graph Problems
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Parameterized Complexity
Subexponential parameterized algorithms on graphs of bounded-genus and H-minor-free graphs
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Polynomial-time data reduction for dominating set
Journal of the ACM (JACM)
The dominating set problem is fixed parameter tractable for graphs of bounded genus
Journal of Algorithms
Approximation algorithms for classes of graphs excluding single-crossing graphs as minors
Journal of Computer and System Sciences
Genus characterizes the complexity of graph problems: some tight results
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
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We describe an algorithm for the dominating set problem withtime complexity O((24g2 + 24g + 1)kn2) for graphs of bounded genus g, where k is the size of the set. It has previously been shown that this problem is fixed parameter tractable for planar graphs. Our method is a refinement of the earlier techniques.