{"paper":{"title":"$(\\delta, \\chi_{_{\\sf FF}})$-bounded families of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Manouchehr Zaker","submitted_at":"2016-05-13T17:40:02Z","abstract_excerpt":"For any graph $G$, the First-Fit (or Grundy) chromatic number of $G$, denoted by $\\chi_{_{\\sf FF}}(G)$, is defined as the maximum number of colors used by the First-Fit (greedy) coloring of the vertices of $G$. We call a family $\\mathcal{F}$ of graphs $(\\delta, \\chi_{_{\\sf FF}})$-bounded if there exists a function $f(x)$ with $f(x)\\rightarrow \\infty$ as $x\\rightarrow \\infty$ such that for any graph $G$ from the family one has $\\chi_{_{\\sf FF}}(G)\\geq f(\\delta(G))$, where $\\delta(G)$ is the minimum degree of $G$. We first give some results concerning $(\\delta, \\chi_{_{\\sf FF}})$-bounded familie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.04267","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"}