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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 $"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1702.00622","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-02-02T11:22:23Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"2c32046e8a8f70326c133440d4b1a1a9bd93e51b41d6ce1796a9cf8716eb59a2","abstract_canon_sha256":"bdb943085a8c9f014251183d2fdc997494586e11d0e611316318c981a2110956"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:45.975155Z","signature_b64":"eOY6C9PWj0wKvotXIkzaj16M8U7wJUIR3MptEFjnx3qUjKghWrDb3dgaOnjOu9QDCL6eIrH05IKAj6/dKhMOCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"772dff086079eadd2d19d503c7fbbdba6867a06023afc60e6b13f96d5d0ff838","last_reissued_at":"2026-05-18T00:23:45.974501Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:45.974501Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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