Fixed-parameter tractability of graph modification problems for hereditary properties
Information Processing Letters
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Discrete Applied Mathematics
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Operations Research Letters
Parameterized Complexity
On Listing, Sampling, and Counting the Chordal Graphs with Edge Constraints
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
Parameterizing above or below guaranteed values
Journal of Computer and System Sciences
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Journal of Discrete Algorithms
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Discrete Applied Mathematics
Iterative Compression for Exactly Solving NP-Hard Minimization Problems
Algorithmics of Large and Complex Networks
Minimum fill-in and treewidth of split+ke and split+kv graphs
Discrete Applied Mathematics
Minimum fill-in and treewidth of split+ke and split+kv graphs
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
On listing, sampling, and counting the chordal graphs with edge constraints
Theoretical Computer Science
Induced packing of odd cycles in planar graphs
Theoretical Computer Science
Isomorphism for graphs of bounded feedback vertex set number
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
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It is known to be NP-hard to decide whether a graph can be made chordal by the deletion of k vertices. Here we present a uniformly polynomial-time algorithm for the problem: the running time is f(k)nα for some constant α not depending on k and some f depending only on k. For large values of n, such an algorithm is much better than trying all the O(nk) possibilities. Therefore, the chordal deletion problem parameterized by the number k of vertices to be deleted is fixed-parameter tractable. This answers an open question of Cai [2].