{"paper":{"title":"Packing chromatic number of subdivisions of cubic graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alexandr Kostochka, J\\'ozsef Balogh, Xujun Liu","submitted_at":"2018-03-07T06:30:01Z","abstract_excerpt":"A packing $k$-coloring of a graph $G$ is a partition of $V(G)$ into sets $V_1,\\ldots,V_k$ such that for each $1\\leq i\\leq k$ the distance between any two distinct $x,y\\in V_i$ is at least $i+1$. The packing chromatic number, $\\chi_p(G)$, of a graph $G$ is the minimum $k$ such that $G$ has a packing $k$-coloring. For a graph $G$, let $D(G)$ denote the graph obtained from $G$ by subdividing every edge. The questions on the value of the maximum of $\\chi_p(G)$ and of $\\chi_p(D(G))$ over the class of subcubic graphs $G$ appear in several papers. Gastineau and Togni asked whether $\\chi_p(D(G))\\leq 5"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.02537","kind":"arxiv","version":2},"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"}