{"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. Each left node $x$ has $d_x \\geq 1$ random right neighbors. The average left degree $\\Delta$ is fixed, $\\Delta \\geq 2$. 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.1506","kind":"arxiv","version":2},"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"}