A Kernel for Convex Recoloring of Weighted Forests
In this paper, we show that the following problem has a kernel of quadratic size: given is a tree T whose vertices have been assigned colors and a non-negative integer weight, and given is an integer k. In a recoloring, the color of some vertices is changed. We are looking for a recoloring such that each color class induces a subtree of T and such that the total weight of all recolored vertices is at most k. Our result generalizes a result by Bodlaender et al.  who give quadratic size kernel for the case that all vertices have unit weight.
- 1.Bachoore, E.H., Bodlaender, H.L.: Convex recoloring of leaf-colored trees. Technical Report UU-CS-2006-010, Department of Information and Computing Sciences, Utrecht University (2006)Google Scholar
- 4.Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer, Heidelberg (1999)Google Scholar
- 5.Flum, J., Grohe, M.: Parameterized Complexity Theory. Springer, Secaucus (2006)Google Scholar