{"paper":{"title":"Reducts of the random bipartite graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Yun Lu","submitted_at":"2011-01-10T20:46:40Z","abstract_excerpt":"Let $\\Gamma$ be the random bipartite graph, a countable graph with two infinite sides, edges randomly distributed between the sides, but no edges within a side. In this paper, we investigate the reducts of $\\Gamma$ that preserve sides. We classify the closed permutation subgroups containing the group $Aut(\\Gamma)^*$, where $Aut(\\Gamma)^*$ is the group of all isomorphisms and anti-isomorphisms of $\\Gamma$ preserving the two sides. Our results rely on a combinatorial theorem of Ne\\v{s}et\\v{r}il-R\\\"{o}dl and a strong finite submodel property for $\\Gamma$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.1947","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"}