Journal of the ACM (JACM)
Finding Even Cycles Even Faster
SIAM Journal on Discrete Mathematics
Proof of a conjecture of Mader, Erdös and Hajnal on topological complete subgraphs
European Journal of Combinatorics
The extremal function for complete minors
Journal of Combinatorial Theory Series B
Dominating sets in planar graphs: branch-width and exponential speed-up
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Improved Parameterized Algorithms for Planar Dominating Set
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
Splitters and near-optimal derandomization
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Generalized hashing and parent-identifying codes
Journal of Combinatorial Theory Series A
Detecting short directed cycles using rectangular matrix multiplication and dynamic programming
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
The dominating set problem is fixed parameter tractable for graphs of bounded genus
Journal of Algorithms
Fixed-parameter algorithms for (k, r)-center in planar graphs and map graphs
ACM Transactions on Algorithms (TALG)
Graph Theory With Applications
Graph Theory With Applications
Subexponential parameterized algorithms on bounded-genus graphs and H-minor-free graphs
Journal of the ACM (JACM)
A refined search tree technique for Dominating Set on planar graphs
Journal of Computer and System Sciences
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Random separation: a new method for solving fixed-cardinality optimization problems
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
Parameterized Complexity
Parameterized Algorithms for Generalized Domination
COCOA 2008 Proceedings of the 2nd international conference on Combinatorial Optimization and Applications
Parameterized Complexity for Domination Problems on Degenerate Graphs
Graph-Theoretic Concepts in Computer Science
The parameterized complexity of editing graphs for bounded degeneracy
Theoretical Computer Science
Kernelization hardness of connectivity problems in d-degenerate graphs
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
Parameterized complexity of generalized domination problems
Discrete Applied Mathematics
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There is substantial literature dealing with fixed parameter algorithms for the dominating set problem on various families of graphs. In this paper, we give a kO(dk)n time algorithm for finding a dominating set of size at most k in a d-degenerated graph with n vertices. This proves that the dominating set problem is fixed-parameter tractable for degenerated graphs. For graphs that do not contain Kh as a topological minor, we give an improved algorithm for the problem with running time (O(h))hkn. For graphs which are Kh-minor-free, the running time is further reduced to (O(log h))hk/2n. Fixed-parameter tractable algorithms that are linear in the number of vertices of the graph were previously known only for planar graphs. For the families of graphs discussed above, the problem of finding an induced cycle of a given length is also addressed. For every fixed H and k, we show that if an H-minor-free graph G with n vertices contains an induced cycle of size k, then such a cycle can be found in O(n) expected time as well as in O(n log n) worst-case time. Some results are stated concerning the (im)possibility of establishing linear time algorithms for the more general family of degenerated graphs.