{"paper":{"title":"The Parameterized Complexity of Happy Colorings","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"I. Vinod Reddy, Neeldhara Misra","submitted_at":"2017-08-13T04:52:27Z","abstract_excerpt":"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 maximises the number of happy vertices (edges). Both problems are known to be NP-hard in general even when $\\ell = 3$, and is polynomially solvable when $\\ell = 2$. In [IWOCA 2016] it was shown that both probl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.03853","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}