Disjoint paths of bounded length in large generalized cycles

Paths of Bounded Length and Their Cuts: Parameterized Complexity and Algorithms

We study the parameterized complexity of two families of problems: the bounded length disjoint paths problem and the bounded length cut problem. From Menger’s theorem both problems are equivalent (and computationally easy) in the unbounded case for single source, single target paths. However, in the bounded case, they are combinatorially distinct and are both NP-hard, even to approximate. Our r...

Approximability of 3- and 4-Hop Bounded Disjoint Paths Problems

A path is said to be `-bounded if it contains at most ` edges. We consider two types of `-bounded disjoint paths problems. In the maximum edgeor node-disjoint path problems MEDP(`) and MNDP(`), the task is to find the maximum number of edgeor node-disjoint `-bounded (s, t)-paths in a given graph G with source s and sink t, respectively. In the weighted edgeor node-disjoint path problems WEDP(`)...

Kernel Bounds for Disjoint Cycles and Disjoint Paths

In this paper, we give evidence for the problems Disjoint Cycles and Disjoint Paths that they cannot be preprocessed in polynomial time such that resulting instances always have a size bounded by a polynomial in a specified parameter (or, in short: do not have a polynomial kernel); these results are assuming the validity of certain complexity theoretic assumptions. We build upon recent results ...

Splitting a graph into disjoint induced paths or cycles

A graph is an X-graph of Y-graphs (or two-level clustered graph) if its vertices can be partitioned into subsets (called clusters) such that each cluster induces a graph belonging to the given class Y and the graph of the clusters belongs to another given class X. Two-level clustered graphs are a useful and interesting concept in graph drawing. We consider the complexity of recognizing two-leve...

Length-bounded disjoint paths in planar graphs