Editing to Connected F-Degree Graph

Editing to Connected f-Degree Graph

In the Edge Editing to Connected f-Degree Graph problem we are given a graph G, an integer k and a function f assigning integers to vertices of G. The task is to decide whether there is a connected graph F on the same vertex set as G, such that for every vertex v, its degree in F is f(v) and the number of edges in E(G)4E(F ), the symmetric difference of E(G) and E(F ), is at most k. We show tha...

Graph Editing to a Given Degree Sequence

We investigate the parameterized complexity of the graph editing problem called Editing to a Graph with a Given Degree Sequence, where the aim is to obtain a graph with a given degree sequence σ by at most k vertex or edge deletions and edge additions. We show that the problem is W[1]-hard when parameterized by k for any combination of the allowed editing operations. From the positive side, we ...

A Degree Condition For Graphs to Have Connected (g, f)-Factors

Editing to a Connected Graph of Given Degrees

The aim of edge editing or modification problems is to change a given graph by adding and deleting of a small number of edges in order to satisfy a certain property. We consider the Edge Editing to a Connected Graph of Given Degrees problem that for a given graph G, non-negative integers d, k and a function δ : V (G) → {1, . . . , d}, asks whether it is possible to obtain a connected graph G′ f...

Simpler Editing of Spatially-Connected Graph Hierarchies using Zipping Algorithms

Graph hierarchies, the data structures that result from hierarchically clustering the nodes of a graph, are widely used as a multi-scale way of representing data in many computing fields, including image segmentation, mesh simplification, hierarchical pathfinding and visualisation. As a result, significant efforts have been made over the years to find ways of constructing ‘good’ graph hierarchi...