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Given a real number $p \\in [0,1]$ such that $d_1 := pn_2$ and $d_2 := pn_1$ are integers, let $R(n,n,p)$ be a random subgraph of $K_{n,n}$ such that every $v \\in V_i$ has degree $d_i$, for $i = 1, 2$. In this paper we determine sufficient conditions on $n_1,n_2,p$, and $m$ under which one can embed $G(n,n,m)$ into $R(n,n,p)$ and vice versa with probability tending to $1$. In particular, in the balanced case $n_1 = n_2$, we show that if $p \\gg \\log"},"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":"2010.15751","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-10-29T16:58:24Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"1f9ada193d64f1d8bd8ffc66607cfe1e0aef41f01731b9c00a492c0b7c2bcc96","abstract_canon_sha256":"b4e4f86c8238206f0fe2389053185e4f0bace28ccaf2af0f7324366110d02b7d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:19:02.255397Z","signature_b64":"J+KAvh6/WCK+82H0/Lpmpw7Ru2g7KfkNfuwNf3yiu/jD7v7GpoB97sfBNW5M/+LjUBxQl8NwluDdx19CosekDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"541f1991ae3ab6bca28f6dfaf534669dba4affe288b9be3f5c054580973aa73a","last_reissued_at":"2026-07-05T03:19:02.254842Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:19:02.254842Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sandwiching biregular random graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Andrzej Ruci\\'nski, Christian Reiher, Matas \\v{S}ileikis, Tereza Klimo\\v{s}ov\\'a","submitted_at":"2020-10-29T16:58:24Z","abstract_excerpt":"Let $G(n,n,m)$ be a uniformly random $m$-edge subgraph of the complete bipartite graph $K_{n,n}$ with bipartition $(V_1, V_2)$, where $n_i = |V_i|$. 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