{"paper":{"title":"Partitioning and coloring with degree constraints","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Landon Rabern","submitted_at":"2012-02-27T08:41:10Z","abstract_excerpt":"We prove that if $G$ is a vertex critical graph with $\\chi(G) \\geq \\Delta(G) + 1 - p \\geq 4$ for some $p \\in \\mathbb{N}$ and $\\omega(\\fancy{H}(G)) \\leq \\frac{\\chi(G) + 1}{p + 1} - 2$, then $G = K_{\\chi(G)}$ or $G = O_5$. Here $\\fancy{H}(G)$ is the subgraph of $G$ induced on the vertices of degree at least $\\chi(G)$. This simplifies and improves the results in the paper of Kostochka, Rabern and Stiebitz \\cite{krs_one}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.5855","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"}