Parameterized complexity of finding subgraphs with hereditary properties
Theoretical Computer Science
Computing small partial coverings
Information Processing Letters
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
Parameterized complexity of generalized vertex cover problems
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
Parameterized Complexity
Parameterized algorithms for the independent set problem in some hereditary graph classes
IWOCA'10 Proceedings of the 21st international conference on Combinatorial algorithms
Intuitive algorithms and t-vertex cover
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Journal of Discrete Algorithms
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We show that several problems that are hard for various parameterized complexity classes on general graphs, become fixed parameter tractable on graphs with no small cycles More specifically, we give fixed parameter algorithms for Dominating Set, t-Vertex Cover (where we need to cover at least t edges) and several of their variants on graphs that have no triangles or cycles of length 4. These problems are known to be W[i]-hard for some i in general graphs. We also show that the Dominating Set problem is W[2]-hard in bipartite graphs and hence on triangle free graphs In the case of Independent Set and several of its variants, we show them fixed parameter tractable even in triangle free graphs. In contrast, we show that the Dense Subgraph problem (related to the Clique problem) is W[1]-hard on graphs with no cycles of length at most 5