{"paper":{"title":"The spectral inducibility of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Liying Kang, Xizhi Liu, Yongchun Lu","submitted_at":"2026-05-29T04:12:48Z","abstract_excerpt":"We introduce a spectral version of the classical inducibility problem. Given an $\\ell$-vertex graph $F$ and an $n$-vertex graph $G$, let $H_F(G)$ be the $\\ell$-uniform hypergraph whose edges are the $\\ell$-sets inducing a copy of $F$ in $G$. We study the maximum possible $\\alpha$-spectral radius of $H_F(G)$ over all $n$-vertex graphs $G$. For fixed $G$, this spectral parameter tends to $\\ell!$ times the number of induced copies of $F$ in $G$ as $\\alpha\\to\\infty$, and therefore refines the usual induced-copy count.\n  Our main result is a spectral analogue of the Brown--Sidorenko reduction: for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.30821","kind":"arxiv","version":1},"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/2605.30821/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"}