{"paper":{"title":"Graphs that are critical for the packing chromatic number","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bo\\v{s}tjan Bre\\v{s}ar, Jasmina Ferme","submitted_at":"2019-04-23T09:07:54Z","abstract_excerpt":"Given a graph $G$, a coloring $c:V(G)\\longrightarrow \\{1,\\ldots,k\\}$ such that $c(u)=c(v)=i$ implies that vertices $u$ and $v$ are at distance greater than $i$, is called a packing coloring of $G$. The minimum number of colors in a packing coloring of $G$ is called the packing chromatic number of $G$, and is denoted by $\\chi_\\rho(G)$. In this paper, we propose the study of $\\chi_\\rho$-critical graphs, which are the graphs $G$ such that for any proper subgraph $H$ of $G$, $\\chi_\\rho(H)<\\chi_\\rho(G)$. We characterize $\\chi_\\rho$-critical graphs with diameter 2, and $\\chi_\\rho$-critical block gra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.10212","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"}