The complexity of regular subgraph recognition
Discrete Applied Mathematics - Computational combinatiorics
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True costs of cheap labor are hard to measure: edge deletion and VCG payments in graphs
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Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
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Information Processing Letters
The parameterized complexity of regular subgraph problems and generalizations
CATS '08 Proceedings of the fourteenth symposium on Computing: the Australasian theory - Volume 77
Finding a Δ-regular supergraph of minimum order
Discrete Applied Mathematics
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IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
Editing graphs to satisfy degree constraints: A parameterized approach
Journal of Computer and System Sciences
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ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
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We study the parameterized complexity of the following problem: is it possible to make a given graph r-regular by applying at most kelementary editing operations; the operations are vertex deletion, edge deletion, and edge addition. We also consider more general annotated variants of this problem, where vertices and edges are assigned an integer cost and each vertex vhas assigned its own desired degree 驴(v) 驴 {0,...,r}. We show that both problems are fixed-parameter tractable when parameterized by (k,r), but W[1]-hard when parameterized by kalone. These results extend our earlier results on problems that are defined similarly but where edge addition is not available. We also show that if edge addition and/or deletion are the only available operations, then the problems are solvable in polynomial time. This completes the classification for all combinations of the three considered editing operations.