{"paper":{"title":"Upper bounds for the 2-hued chromatic number of graphs in terms of the independence number","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Ali Dehghan, Arash Ahadi","submitted_at":"2009-11-21T20:09:24Z","abstract_excerpt":"A 2-hued coloring of a graph $G$ (also known as conditional $(k, 2)$-coloring and dynamic coloring) is a coloring such that for every vertex $v\\in V(G)$ of degree at least $2$, the neighbors of $v$ receive at least $2$ colors. The smallest integer $k$ such that $G$ has a 2-hued coloring with $ k $ colors, is called the {\\it 2-hued chromatic number} of $G$ and denoted by $\\chi_2(G)$. In this paper, we will show that if $G$ is a regular graph, then $ \\chi_{2}(G)- \\chi(G) \\leq 2 \\log _{2}(\\alpha(G)) +\\mathcal{O}(1) $ and if $G$ is a graph and $\\delta(G)\\geq 2$, then $ \\chi_{2}(G)- \\chi(G) \\leq 1+"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.4199","kind":"arxiv","version":5},"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"}