The Convex Recoloring (CR) problem measures how far a tree of characters differs from exhibiting a so‐called ‘perfect phylogeny’. For an input consisting of a vertex‐colored tree T, the problem is to determine whether recoloring at most k vertices can achieve a convex coloring, meaning by this a coloring where each color class induces a subtree. The problem was introduced by Moran and Snir (2007, 2008) who showed that CR is NP‐hard, and described a search‐tree based FPT algorithm with a running time of O(k(k/log k)
k
n
4). The Moran and Snir result did not provide any nontrivial kernelization. In this paper, we show that CR has a kernel of size O(k
2).
