{"paper":{"title":"Chromatic bounds for some classes of $2K_2$-free graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Suchismita Mishra, T. Karthick","submitted_at":"2017-02-02T11:22:23Z","abstract_excerpt":"A hereditary class $\\mathcal{G}$ of graphs is $\\chi$-bounded if there is a $\\chi$-binding function, say $f$ such that $\\chi(G) \\leq f(\\omega(G))$, for every $G \\in \\cal{G}$, where $\\chi(G)$ ($\\omega(G)$) denote the chromatic (clique) number of $G$. It is known that for every $2K_2$-free graph $G$, $\\chi(G) \\leq \\binom{\\omega(G)+1}{2}$, and the class of ($2K_2, 3K_1$)-free graphs does not admit a linear $\\chi$-binding function. In this paper, we are interested in classes of $2K_2$-free graphs that admit a linear $\\chi$-binding function. We show that the class of ($2K_2, H$)-free graphs, where $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.00622","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"}