{"paper":{"title":"Notes on complexity of packing coloring","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO"],"primary_cat":"cs.CC","authors_text":"Bernard Lidick\\'y, Florian Pfender, Minki Kim, Tom\\'a\\v{s} Masa\\v{r}\\'ik","submitted_at":"2017-12-22T10:00:07Z","abstract_excerpt":"A packing $k$-coloring for some integer $k$ of a graph $G=(V,E)$ is a mapping\n  $\\varphi:V\\to\\{1,\\ldots,k\\}$ such that any two vertices $u, v$ of color $\\varphi(u)=\\varphi(v)$ are in distance at least $\\varphi(u)+1$. This concept is motivated by frequency assignment problems. The \\emph{packing chromatic number} of $G$ is the smallest $k$ such that there exists a packing $k$-coloring of $G$.\n  Fiala and Golovach showed that determining the packing chromatic number for chordal graphs is \\NP-complete for diameter exactly 5. While the problem is easy to solve for diameter 2, we show \\NP-completene"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.08373","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"}