Measuring indifference: unit interval vertex deletion
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
A Complexity Dichotomy for Finding Disjoint Solutions of Vertex Deletion Problems
ACM Transactions on Computation Theory (TOCT)
Parameterized complexity of vertex deletion into perfect graph classes
FCT'11 Proceedings of the 18th international conference on Fundamentals of computation theory
A parameterized algorithm for chordal sandwich
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
Parameterized complexity of eulerian deletion problems
WG'11 Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science
Contracting graphs to paths and trees
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Graph minors and parameterized algorithm design
The Multivariate Algorithmic Revolution and Beyond
Faster parameterized algorithms for deletion to split graphs
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
Kernel lower bounds using co-nondeterminism: finding induced hereditary subgraphs
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
A polynomial kernel for proper interval vertex deletion
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
Split Vertex Deletion meets Vertex Cover: New fixed-parameter and exact exponential-time algorithms
Information Processing Letters
Satisfiability of acyclic and almost acyclic CNF formulas
Theoretical Computer Science
Finding small separators in linear time via treewidth reduction
ACM Transactions on Algorithms (TALG)
A faster FPT algorithm for Bipartite Contraction
Information Processing Letters
Parameterized complexity of vertex deletion into perfect graph classes
Theoretical Computer Science
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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 or by the deletion of k edges. Here we present a uniformly polynomial-time algorithm for both problems: the running time is f(k)⋅n α 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(n k ) possibilities. Therefore, the chordal deletion problem parameterized by the number k of vertices or edges to be deleted is fixed-parameter tractable. This answers an open question of Cai (Discrete Appl. Math. 127:415–429, 2003).