A Kernel for Convex Recoloring of Weighted Forests
- Cite this paper as:
- Bodlaender H.L., Comas M. (2010) A Kernel for Convex Recoloring of Weighted Forests. In: van Leeuwen J., Muscholl A., Peleg D., Pokorný J., Rumpe B. (eds) SOFSEM 2010: Theory and Practice of Computer Science. SOFSEM 2010. Lecture Notes in Computer Science, vol 5901. Springer, Berlin, Heidelberg
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.
Unable to display preview. Download preview PDF.