{"paper":{"title":"Packing coloring of some undirected and oriented coronae graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Eric Sopena (LaBRI), Isma Bouchemakh (L'IFORCE), La\\\"iche Daouya (L'IFORCE)","submitted_at":"2015-06-24T06:03:18Z","abstract_excerpt":"The packing chromatic number $\\pcn(G)$ of a graph $G$ is the smallest integer $k$ such that its set of vertices $V(G)$ can be partitioned into $k$ disjoint subsets $V\\_1$, \\ldots, $V\\_k$, in such a way that every two distinct vertices in $V\\_i$ are at distance greater than $i$ in $G$ for every $i$, $1\\le i\\le k$.\nFor a given integer $p \\ge 1$, the generalized corona $G\\odot pK\\_1$ of a graph $G$ is the graph obtained from $G$ by adding $p$ degree-one neighbors to every vertex  of $G$.\nIn this paper, we determine the packing chromatic number of generalized coronae of paths and cycles.\nMoreover,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.07248","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"}