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Secondly, we prove that for each $t \\geq 2$, every graph with no odd $K_t$ minor has a partition of its vertex set into $10t-13$ sets $V_1, \\dots, V_{10t-13}$ such that each $V_i$ induces a s"},"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":"1612.05372","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-12-16T05:30:52Z","cross_cats_sorted":[],"title_canon_sha256":"1280155948142077a615329644d918405aa3d23845bdcf8057615940fcd4bb22","abstract_canon_sha256":"dfd1c70b9a4baea1f6907813fa2f46328bea9fc28838d1abe09265a13ac6f577"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:24.024808Z","signature_b64":"Qt5JsNmpXa6wWYVctIyv38Rtp4fPs5g0nGioYaBNECu+g4xdu9HzzAIgv5lpO/co8ZMDP1xoGogpyj5sJH5RCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cecb52e947b6830ba811692eb9389e57919725131c195eed30f2abef6fa5e3f1","last_reissued_at":"2026-05-17T23:43:24.024216Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:24.024216Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Improper coloring of graphs with no odd clique minor","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dong Yeap Kang, Sang-il Oum","submitted_at":"2016-12-16T05:30:52Z","abstract_excerpt":"As a strengthening of Hadwiger's conjecture, Gerards and Seymour conjectured that every graph with no odd $K_t$ minor is $(t-1)$-colorable. 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