Fixed-parameter tractability of graph modification problems for hereditary properties
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)
Interval Completion Is Fixed Parameter Tractable
SIAM Journal on Computing
Planarity Allowing Few Error Vertices in Linear Time
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Chordal Deletion is Fixed-Parameter Tractable
Algorithmica
Improved upper bounds for vertex cover
Theoretical Computer Science
Measuring indifference: unit interval vertex deletion
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
Parameterized complexity of vertex deletion into perfect graph classes
FCT'11 Proceedings of the 18th international conference on Fundamentals of computation theory
Obtaining a Planar Graph by Vertex Deletion
Algorithmica
Faster parameterized algorithms for deletion to split graphs
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
| Hi-index | 0.89 |
In the Split Vertex Deletion problem, given a graph G and an integer k, we ask whether one can delete k vertices from the graph G to obtain a split graph (i.e., a graph, whose vertex set can be partitioned into two sets: one inducing a clique and the second one inducing an independent set). In this paper we study exact (exponential-time) and fixed-parameter algorithms for Split Vertex Deletion.*We show that, up to a factor quasipolynomial in k and polynomial in n, the Split Vertex Deletion problem can be solved in the same time as the well-studied Vertex Cover problem. By plugging in the currently best fixed-parameter algorithm for Vertex Cover due to Chen et al. [Theor. Comput. Sci. 411 (40-42) (2010) 3736-3756], we obtain an algorithm that solves Split Vertex Deletion in time O(1.2738^kk^O^(^l^o^g^k^)+n^3). *We show that all maximal induced split subgraphs of a given n-vertex graph can be listed in O(3^n^/^3n^O^(^l^o^g^n^)) time. To achieve our goals, we prove the following structural result that may be of independent interest: for any graph G we may compute a family P of size n^O^(^l^o^g^n^) containing partitions of V(G) into two parts, such that for any two disjoint sets X"C,X"I@?V(G) where G[X"C] is a clique and G[X"I] is an independent set, there is a partition in P which contains all vertices of X"C on one side and all vertices of X"I on the other. Moreover, the family P can be enumerated in O(n^O^(^l^o^g^n^)) time.