1.5-Approximation Algorithm for the 2-Convex Recoloring Problem.

Given a graph (G = (V, E)), a coloring function (chi : V rightarrow C), assigning each vertex a color, is called convex if, for every color (c in C), the set of vertices with color c induces a connected subgraph of G. In the Convex Recoloring problem a colored graph (G_chi ) is given, and the goal is to find a convex coloring (chi u0027) of G that recolors a minimum number of vertices. The 2-Convex Recoloring problem (2-CR) is the special case, where the given coloring (chi ) assigns the same color to at most two vertices. 2-CR is known to be NP-hard even if G is a path.