Abstract
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. [3] who give quadratic size kernel for the case that all vertices have unit weight.
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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. https://doi.org/10.1007/978-3-642-11266-9_18
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DOI: https://doi.org/10.1007/978-3-642-11266-9_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-11265-2
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