{"paper":{"title":"The binomial random graph is a bad inducer","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Fan Wei, Marcus Michelen, Vishesh Jain","submitted_at":"2023-06-22T16:23:21Z","abstract_excerpt":"For a finite graph $F$ and a value $p \\in [0,1]$, let $I(F,p)$ denote the largest $y$ for which there is a sequence of graphs of edge density approaching $p$ so that the induced $F$-density of the sequence approaches $y$. We show that for all $F$ on at least three vertices and all $p \\in (0,1)$, the binomial random graph $G(n,p)$ has induced $F$-density strictly less than $I(F,p).$ This provides a negative answer to a problem posed by Liu, Mubayi and Reiher.\n  Our approach is in the limiting setting of graphons, and we in fact show a stronger result: the binomial random graph is never a \\emph{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.13014","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2306.13014/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}