Editing graphs to satisfy degree constraints: A parameterized approach

Luke Mathieson, Stefan Szeider
2012 Journal of computer and system sciences (Print)  
We study a wide class of graph editing problems that ask whether a given graph can be modified to satisfy certain degree constraints, using a limited number of vertex deletions, edge deletions, or edge additions. The problems generalize several well-studied problems such as the General Factor Problem and the Regular Subgraph Problem. We classify the parameterized complexity of the considered problems taking upper bounds on the number of editing steps and the maximum degree of the resulting
more » ... as parameters. • We consider several editing operations including edge addition, so that in some cases the obtained graph is not a subgraph of the given graph. In particular we consider the editing operations vertex deletion (denoted v), edge deletion (denoted e), and edge addition (denoted a). • Each vertex v of the given graph has assigned a list δ(v) of numbers; after the editing process the degree of the vertex must belong to its list. For example, by assigning all vertices the list {r} we can force the target graph to be r-regular. By allowing arbitrary lists we can express variants of the General Factor problem introduced and studied by Lovász [19, 20] . • Vertices and edges can have positive integer weights, giving each edit operation a certain cost. ✩ This paper contains results that were published in preliminary form in Mathieson and Szeider (2008) [23,24].
doi:10.1016/j.jcss.2011.02.001 fatcat:fljdtrsj4jfpfidlwcekot7zuu