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The well-known Erd\\H{o}s-Lov\\'asz Tihany Conjecture from 1968 states that every graph $G$ with $\\omega(G) < \\chi(G) = s + t - 1$ is $(s,t)$-splittable. This conjecture is hard, and few related results are known. However, it has been verified to be true for line graphs, quasi-line graphs, and graphs with independence number $2$. In this paper, we establish"},"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":"1805.11437","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-05-27T14:05:48Z","cross_cats_sorted":[],"title_canon_sha256":"e8c581894a3702e7e098875d1b40520ac3aeaaa7e0c5e7623c2609bb62d5753e","abstract_canon_sha256":"2709957cab4d161f836f61abfa0958903000307c66dab0a1d5c1a03b43bc68d0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:42.561216Z","signature_b64":"HIz2cPhm8auL2O46t8O1Mx0f3WMn9dilqgBH5JscS72B8Khu/lJrC8Sc7x2ABAjsv5BzA4W1otAX80xzBc5UCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"39ac5d82d727023047a85891e840a45903616896ef288a6c56c339421b0cbecb","last_reissued_at":"2026-05-18T00:14:42.560627Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:42.560627Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Erd\\H{o}s-Lov\\'asz Tihany Conjecture for graphs with forbidden holes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Zi-Xia Song","submitted_at":"2018-05-27T14:05:48Z","abstract_excerpt":"A hole in a graph is an induced cycle of length at least $4$. Let $s\\ge2$ and $t\\ge2$ be integers. A graph $G$ is $(s,t)$-splittable if $V(G)$ can be partitioned into two sets $S$ and $T$ such that $\\chi(G[S ]) \\ge s$ and $\\chi(G[T ]) \\ge t$. The well-known Erd\\H{o}s-Lov\\'asz Tihany Conjecture from 1968 states that every graph $G$ with $\\omega(G) < \\chi(G) = s + t - 1$ is $(s,t)$-splittable. This conjecture is hard, and few related results are known. However, it has been verified to be true for line graphs, quasi-line graphs, and graphs with independence number $2$. 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