# The Parameterized Complexity of Happy Colorings

@inproceedings{Misra2017ThePC,
title={The Parameterized Complexity of Happy Colorings},
author={Neeldhara Misra and I. Vinod Reddy},
booktitle={IWOCA},
year={2017}
}
• Published in IWOCA 17 July 2017
• Mathematics
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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