TREEWIDTH and PATHWIDTH parameterized by vertex cover
Mathieu Chapelle (1), Mathieu Liedloff (2), Ioan Todinca (2), and, Yngve Villanger (3) ((1) University Paris Est, France, (2) University of, Orleans, France, (3) University of Bergen, Norway)
TL;DR
This paper investigates the computational complexity of TREEWIDTH and PATHWIDTH problems when parameterized by the size of a minimum vertex cover, providing algorithms with exponential time bounds and relating to kernelization results.
Contribution
It presents algorithms for computing TREEWIDTH and PATHWIDTH in O*(3^k) time when parameterized by vertex cover size, extending the understanding of these problems' complexity.
Findings
PATHWIDTH and TREEWIDTH are computable in O*(3^k) time with vertex cover parameter
Results complement existing polynomial kernel results for these parameters
Enhances understanding of parameterized complexity for graph width parameters
Abstract
After the number of vertices, Vertex Cover is the largest of the classical graph parameters and has more and more frequently been used as a separate parameter in parameterized problems, including problems that are not directly related to the Vertex Cover. Here we consider the TREEWIDTH and PATHWIDTH problems parameterized by k, the size of a minimum vertex cover of the input graph. We show that the PATHWIDTH and TREEWIDTH can be computed in O*(3^k) time. This complements recent polynomial kernel results for TREEWIDTH and PATHWIDTH parameterized by the Vertex Cover.
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Taxonomy
TopicsAdvanced Graph Theory Research · Complexity and Algorithms in Graphs · Graph Labeling and Dimension Problems