The Parameterized Complexity of Happy Colorings

  title={The Parameterized Complexity of Happy Colorings},
  author={Neeldhara Misra and I. Vinod Reddy},
Consider a graph \(G = (V,E)\) and a coloring c of vertices with colors from \([\ell ]\). A vertex v is said to be happy with respect to c if \(c(v) = c(u)\) for all neighbors u of v. Further, an edge (u, v) is happy if \(c(u) = c(v)\). Given a partial coloring c of V, the Maximum Happy Vertex (Edge) problem asks for a total coloring of V extending c to all vertices of V that maximizes the number of happy vertices (edges). Both problems are known to be NP-hard in general even when \(\ell = 3… 
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