Introduction to algorithms
Vertex cover: further observations and further improvements
Journal of Algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Practical Algorithms on Partial k-Trees with an Application to Domination-like Problems
WADS '93 Proceedings of the Third Workshop on Algorithms and Data Structures
Improved Tree Decomposition Based Algorithms for Domination-like Problems
LATIN '02 Proceedings of the 5th Latin American Symposium on Theoretical Informatics
Graph Minors. XX. Wagner's conjecture
Journal of Combinatorial Theory Series B - Special issue dedicated to professor W. T. Tutte
Finding k disjoint triangles in an arbitrary graph
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
Linear kernels in linear time, or how to save k colors in O(n2) steps
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
Parameterized Complexity
Theoretical Computer Science - Parameterized and exact computation
Algorithm for Finding k-Vertex Out-trees and Its Application to k-Internal Out-branching Problem
COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
Better Approximation Algorithms for the Maximum Internal Spanning Tree Problem
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
Minimum leaf out-branching and related problems
Theoretical Computer Science
A Linear Vertex Kernel for Maximum Internal Spanning Tree
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Algorithm for finding k-vertex out-trees and its application to k-internal out-branching problem
Journal of Computer and System Sciences
Sharp separation and applications to exact and parameterized algorithms
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Towards a taxonomy of techniques for designing parameterized algorithms
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
On the directed Full Degree Spanning Tree problem
Discrete Optimization
A linear vertex kernel for maximum internal spanning tree
Journal of Computer and System Sciences
Beyond bidimensionality: Parameterized subexponential algorithms on directed graphs
Information and Computation
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The k-INTERNAL SPANNING TREE problem asks whether a certain graph G has a spanning tree with at least k internal vertices. Basing our work on the results presented in [Prieto and Sloper 2003], we show that there exists a set of reduction rules that modify an arbitrary spanning tree of a graph into a spanning tree with no induced edges between the leaves. Thus, the rules either produce a tree with many internal vertices, effectively deciding the problem, or they identify a large independent set, the leaves, in the graph. Having a large independent set is beneficial, because then the graph allows both 'crown decompositions' and path decompositions. We show how this crown decomposition can be used to obtain a O(k2) kernel for the k-INTERNAL SPANNING TREE problem, improving on the O(k3) kernel presented in [Prieto and Sloper 2003].