{"paper":{"title":"Spectral Tur\\'an-type problem in non-$r$-partite graphs: Forbidden generalized book graph $B_{r,k}$","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Shuchao Li, Yuantian Yu","submitted_at":"2025-08-16T13:18:49Z","abstract_excerpt":"Given a graph $H$, a graph is said to be $H$-free if it does not contain $H$ as a subgraph. A graph is color-critical when it has an edge whose removal leads to a reduction in its chromatic number. For a graph $H$ with a chromatic number of \\(r + 1\\), we use \\(\\text{spex}_{r + 1}(n, H)\\) to represent the maximum spectral radius among non-$r$-partite $H$-free graphs of order $n$. The set of all non-$r$-partite $H$-free graphs of order $n$ that have a spectral radius of \\(\\text{spex}_{r + 1}(n, H)\\) is denoted as \\(\\text{SPEX}_{r + 1}(n, H)\\). For \\(r\\geq2\\) and \\(k\\geq1\\), we define \\(B_{r,k}\\)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.12034","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/2508.12034/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"}