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So far, the most general result says that every graph with no odd $K_t$-minor is $O(t \\sqrt{\\log t})$-colorable.\n  In this paper, we tackle this conjecture from an algorithmic view, and show the following:\n  For a given graph $G$ and any fixed $t$, there is a polynomial time algorithm to output one of the foll"},"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":"1508.04053","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-08-17T15:15:24Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"16464bf8837606ac51ef4c5b507fcd9e1c1a607b68c9d9406b2348a35bd7412d","abstract_canon_sha256":"d8e6854d24233f173ad3b34dc0be8bb8c9dd3236f101f18fe576953108e7d3c9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:12.926692Z","signature_b64":"8VWgyy3XWyLFZGs7xl9AWi2J5rXD5qVOB5LnVHfWOkAc+fMbADF7lrp5nB/BXpRwpHJlkL3/p3gLUnPWe/a1Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fecd424438a220f78a77b504ae1a2a415feb7164b2d3d5fab1e2714ca66814be","last_reissued_at":"2026-05-18T01:35:12.926092Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:12.926092Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The odd Hadwiger's conjecture is \"almost'' decidable","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Ken-ichi Kawarabayashi","submitted_at":"2015-08-17T15:15:24Z","abstract_excerpt":"The odd Hadwiger's conjecture, made by Gerads and Seymour in early 1990s, is an analogue of the famous Hadwiger's conjecture. 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So far, the most general result says that every graph with no odd $K_t$-minor is $O(t \\sqrt{\\log t})$-colorable.\n  In this paper, we tackle this conjecture from an algorithmic view, and show the following:\n  For a given graph $G$ and any fixed $t$, there is a polynomial time algorithm to output one of the foll"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.04053","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1508.04053","created_at":"2026-05-18T01:35:12.926173+00:00"},{"alias_kind":"arxiv_version","alias_value":"1508.04053v1","created_at":"2026-05-18T01:35:12.926173+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.04053","created_at":"2026-05-18T01:35:12.926173+00:00"},{"alias_kind":"pith_short_12","alias_value":"73GUERBYUIQP","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_16","alias_value":"73GUERBYUIQPPCTX","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_8","alias_value":"73GUERBY","created_at":"2026-05-18T12:29:07.941421+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/73GUERBYUIQPPCTXWUCK4GRKIF","json":"https://pith.science/pith/73GUERBYUIQPPCTXWUCK4GRKIF.json","graph_json":"https://pith.science/api/pith-number/73GUERBYUIQPPCTXWUCK4GRKIF/graph.json","events_json":"https://pith.science/api/pith-number/73GUERBYUIQPPCTXWUCK4GRKIF/events.json","paper":"https://pith.science/paper/73GUERBY"},"agent_actions":{"view_html":"https://pith.science/pith/73GUERBYUIQPPCTXWUCK4GRKIF","download_json":"https://pith.science/pith/73GUERBYUIQPPCTXWUCK4GRKIF.json","view_paper":"https://pith.science/paper/73GUERBY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1508.04053&json=true","fetch_graph":"https://pith.science/api/pith-number/73GUERBYUIQPPCTXWUCK4GRKIF/graph.json","fetch_events":"https://pith.science/api/pith-number/73GUERBYUIQPPCTXWUCK4GRKIF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/73GUERBYUIQPPCTXWUCK4GRKIF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/73GUERBYUIQPPCTXWUCK4GRKIF/action/storage_attestation","attest_author":"https://pith.science/pith/73GUERBYUIQPPCTXWUCK4GRKIF/action/author_attestation","sign_citation":"https://pith.science/pith/73GUERBYUIQPPCTXWUCK4GRKIF/action/citation_signature","submit_replication":"https://pith.science/pith/73GUERBYUIQPPCTXWUCK4GRKIF/action/replication_record"}},"created_at":"2026-05-18T01:35:12.926173+00:00","updated_at":"2026-05-18T01:35:12.926173+00:00"}