1. Length-bounded cuts: Proper interval graphs and structural parameters.
- Author
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Bentert, Matthias, Heeger, Klaus, and Knop, Dušan
- Subjects
- *
CHARTS, diagrams, etc. , *CUTTING stock problem , *INTEGERS , *LOGICAL prediction - Abstract
We study the Length-Bounded Cut problem for special graph classes and from a parameterized complexity viewpoint. Here, we are given a graph G , two vertices s and t , and positive integers β and λ. The task is to find a set F of at most β edges such that each s - t -path of length at most λ in G contains some edge in F. Bazgan et al. [20] conjectured that Length-Bounded Cut admits a polynomial-time algorithm if the input graph is a proper interval graph. We confirm this conjecture by providing a dynamic-programming-based polynomial-time algorithm. Moreover, we strengthen the W[1]-hardness result of Dvořák and Knop [15] for Length-Bounded Cut parameterized by pathwidth by showing W[1]-hardness for the combined parameter pathwidth and maximum degree of the input graph. Finally, we prove that Length-Bounded Cut is W[1]-hard for the feedback vertex number. Both our hardness results complement known XP algorithms. [ABSTRACT FROM AUTHOR]
- Published
- 2022
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