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These, together with the case $L(G)=\\{3,5\\}$ solved in \\cite{W}, give a complete solution to the general problem addressed in \\cite{W,CS,KRS}. Our results also improve a classical theorem of Gy\\'{a}rf\\'{a}s which asserts that $\\chi(G)\\le 2|L(G)|+2$ for any graph $G$."},"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":"1512.06393","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-12-20T16:10:44Z","cross_cats_sorted":[],"title_canon_sha256":"1fbfa136af15b75176c1ac7651fe949df65221f5ffe934a290a8b5b0cba09dd2","abstract_canon_sha256":"94ce25dbb6563ba840c1fe1846400ccf54126dc30578447fe7161b8904cbdd5f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:45.427002Z","signature_b64":"4aB1VYQB/L7yBMJ3296uzPqpPwkJW1fqNrqY3c3PV7Q+iEwAv051Lkd1jd/URYAb3t2fpzs21pq2ZkYXGr5WBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ee4f924b10fc694d3ed8fb6bc369ba8d89d62243cac2a9e0983b604b9d8732c7","last_reissued_at":"2026-05-18T00:24:45.426411Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:45.426411Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Coloring graphs with two odd cycle lengths","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bo Ning, Jie Ma","submitted_at":"2015-12-20T16:10:44Z","abstract_excerpt":"In this paper we determine the chromatic number of graphs with two odd cycle lengths. 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