In a clustering problem one has to partition a set of elements into homogeneous and well-separated subsets. From a graph theoretic point of view, a cluster graph is a vertex-disjoint union of cliques. The clustering problem is the task of making fewest changes to the edge set of an input graph so that it becomes a cluster graph. We study the complexity of three variants of the problem. In the C...

This report documents the program and the outcomes of Dagstuhl Seminar 14071 “Graph Modification Problems”. The seminar was held from February 9 to February 14, 2014. This report contains abstracts for presentations about the recent developments on algorithms and structural results for graph modification problems, as well as related areas. Furthermore, the report contains a summary of open prob...

i Acknowledgements The first person I need to thank is my supervisor Pinar Heggernes. Without her guidance, encouragement and scolding from time to time, this work would not exist. Thank you for taking me as your student, teaching me so much and believing in me from the very start. I have never told you how much this meant to me, but I hope this thesis can make up for at least some of it. These...

In this work, we introduce a similarity-network-based approach to explore the role of interacting single-cell histone modification signals in haematopoiesis—the process differentiation blood cells. Histones are proteins that provide structural support chromosomes. They subject chemical modifications—acetylation or methylation—that affect degree accessibility genes and, turn, formation different...

In graph modification problems, one is given a graph G and the goal is to apply a minimum number of modification operations (such as edge deletions) to G such that the resulting graph fulfills a certain property. For example, the Cluster Deletion problem asks to delete as few edges as possible such that the resulting graph is a disjoint union of cliques. Graph modification problems appear in nu...

We study the complexity of graph modification problems with respect to homomorphism-based colouring properties edge-coloured graphs. A homomorphism from $G$ $H$ is a vertex-mapping that preserves adjacencies and edge-colours. consider property having fixed $H$. The question we are interested in is: given an $G$, can perform $k$ operations so resulting admits $H$? vertex-deletion, edge-deletion ...