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We show that for any $K_{3,3}$-minor-free graph $G$, $AT(G)\\le 5$, there exists a matching $M$ and a forest $F$ such that $AT(G-M)\\le 4$ and $AT(G-E(F))\\le 3$, extending the result on the Alon-Tarsi number of $K_5$-minor-free graphs due to Abe, Kim and Ozeki."},"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":"2310.07445","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2023-10-11T12:48:32Z","cross_cats_sorted":[],"title_canon_sha256":"af93bde5da726a98d26ac6fc564b5c7f5fadc37c98af93ff2ac2bc3496753ffb","abstract_canon_sha256":"158d65d468d37a960f036894b7deb24ebbb19a02e26528bba6207788e76bb8a8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:01:06.926794Z","signature_b64":"f9+pr6Jpq2Vy0QfiCTAc06XOPDn4dUo0dwW195QD4tJotc6OjjW+N8jkxs4M56hmDv8o1Q09blTuZhXR+ZQJCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fcddf2a1777046b7a0954165d55312c5a4db08836ff2b1da9a7bf27ac7d8e706","last_reissued_at":"2026-07-05T07:01:06.926350Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:01:06.926350Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Alon-Tarsi number of $K_{3,3}$-minor-free graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bo Zhou, Leyou Xu","submitted_at":"2023-10-11T12:48:32Z","abstract_excerpt":"The well known Wagner's theorem states that a graph is a planar graph if and only if it is $K_5$-minor-free and $K_{3,3}$-minor-free. 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