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We ask whether for the probability that $G$ has a left-perfect matching it is advantageous not to fix $d_x$ for each left node $x$ but rather choose it at random according to some (cleverly chosen) distribution. We show the following, provided that the degrees of the left nodes are independent: If $\\Delta$ is an integer then it is optimal to use a fixed degree of $\\Delta$ for all"},"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":"1203.1506","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-03-07T15:48:24Z","cross_cats_sorted":[],"title_canon_sha256":"a5d8175dc964c5cc8ea2233ab37806a0723c479e52259f626ccc0c65a9f366aa","abstract_canon_sha256":"f002da2a46055cfb0cbe69252cec4f7c4d0bf01946f2c97568c0d4ba198300b1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:56:47.387697Z","signature_b64":"Wc68HQLuUw1mWjwQwkgGAYfmbwqR98BngehrPExS5vbdLLz5Nqh4ReB+53aIsqblEVaNsUHxE/16A2Sb+b98Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"659ebb561a652dffb124408a792020efcae629662f6e553ccd66d270c6fd4052","last_reissued_at":"2026-05-18T03:56:47.387066Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:56:47.387066Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Towards Optimal Degree-distributions for Left-perfect Matchings in Random Bipartite Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Martin Dietzfelbinger, Michael Rink","submitted_at":"2012-03-07T15:48:24Z","abstract_excerpt":"Consider a random bipartite multigraph $G$ with $n$ left nodes and $m \\geq n \\geq 2$ right nodes. 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