Editing to a Connected Graph of Given Degrees

Abstract

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′ from G such that the degree of v is δ(v) for any vertex v by at most k edge editing operations. As the problem is NP-complete even if δ(v) = 2, we are interested in the parameterized complexity and show that Edge Editing to a Connected Graph of Given Degrees admits a polynomial kernel when parameterized by d + k. For the special case δ(v) = d, i.e., when the aim is to obtain a connected d-regular graph, the problem is shown to be fixed parameter tractable when parameterized by k only.KeywordsBipartite GraphConnected GraphParameterized ComplexityPolynomial KernelEdge AdditionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.