Parameterized complexity of multi-node hubs

Parameterized Complexity of Critical Node Cuts

We consider the following natural graph cut problem called Critical Node Cut (CNC): Given a graph G on n vertices, and two positive integers k and x, determine whether G has a set of k vertices whose removal leaves G with at most x connected pairs of vertices. We analyze this problem in the framework of parameterized complexity. That is, we are interested in whether or not this problem is solva...

On the complexity of multi-parameterized cluster editing

The Cluster Editing problem seeks a transformation of a given undirected graph into a disjoint union of cliques via a minimum number of edge additions or deletions. A multi-parameterized version of the problem is studied, featuring a number of input parameters that bound the amount of both edge-additions and deletions per single vertex, as well as the size of a clique-cluster. We show that the ...

On parameterized complexity of the Multi-MCS problem

We introduce the maximum common subgraph problem for multiple graphs (Multi-MCS) inspired by various biological applications such as multiple alignments of gene sequences, protein structures, metabolic pathways, or protein–protein interaction networks. MultiMCS is a generalization of the two-graph Maximum Common Subgraph problem (MCS). On the basis of the framework of parameterized complexity t...

Parameterized complexity of firefighting

The Firefighter problem is to place firefighters on the vertices of a graph to prevent a fire with known starting point from lighting up the entire graph. In each time step, a firefighter may be placed on an unburned vertex, permanently protecting it, and the fire spreads to all neighboring unprotected vertices of burning vertices. The goal is to let as few vertices burn as possible. This probl...

Complexity of Parameterized Counting