How to allocate network centers
Journal of Algorithms
Fixed-parameter tractability and completeness II: on completeness for W[1]
Theoretical Computer Science
Fixed-Parameter Tractability and Completeness I: Basic Results
SIAM Journal on Computing
The extremal function for complete minors
Journal of Combinatorial Theory Series B
Information Processing Letters
Fixed-parameter algorithms for (k, r)-center in planar graphs and map graphs
ACM Transactions on Algorithms (TALG)
Subexponential parameterized algorithms on bounded-genus graphs and H-minor-free graphs
Journal of the ACM (JACM)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
LICS '07 Proceedings of the 22nd Annual IEEE Symposium on Logic in Computer Science
Parameterized Complexity of Vertex Cover Variants
Theory of Computing Systems
Partial vs. Complete Domination: t-Dominating Set
SOFSEM '07 Proceedings of the 33rd conference on Current Trends in Theory and Practice of Computer Science
Linear time algorithms for finding a dominating set of fixed size in degenerated graphs
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
Parameterized Complexity
Kernelization hardness of connectivity problems in d-degenerate graphs
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
Implicit branching and parameterized partial cover problems
Journal of Computer and System Sciences
External-memory network analysis algorithms for naturally sparse graphs
ESA'11 Proceedings of the 19th European conference on Algorithms
Kernelization hardness of connectivity problems in d-degenerate graphs
Discrete Applied Mathematics
Polynomial kernels for dominating set in graphs of bounded degeneracy and beyond
ACM Transactions on Algorithms (TALG)
FPT algorithms for domination in biclique-free graphs
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
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Domination problems are one of the classical types of problems in computer science. These problems are considered in many different versions and on different classes of graphs. We explore the boundary between fixed-parameter tractable and W-hard problems on sparse graphs. More precisely, we expand the list of domination problems which are fixed-parameter tractable(FPT) for degenerate graphs by proving that Connected k -Dominating set and k -Dominating threshold set are FPT. From the other side we prove that there are domination problems which are difficult (W[1] or W[2]-hard) for this graph class. The Partial k -dominating set and (k ,r )-Center for r *** 2 are examples of such problems. It is also remarked that domination problems become difficult for graphs of bounded average degree.