{"paper":{"title":"A Spectral Tur\\'an Problem for a Fixed Tree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bahareh Kudarzi, Dheer Noal Desai, Hemanshu Kaul","submitted_at":"2025-05-20T21:02:42Z","abstract_excerpt":"We study the spectral Tur\\'an problem for trees. To avoid limiting our perspective to specific families of trees, we parametrize trees in terms of their unique bipartition. We say $T \\in \\mathcal{T}_{m,l+1}^{\\delta}$ if $T$ is a tree of order $m$, where the order of the smaller partite set $A$ of $T$ is $l+1$, and $\\delta$ is the minimum degree of the vertices in $A$. The motivation for this parametrization comes from the recent proof of the spectral Erd\\H{o}s-S\\'os conjecture. For a given fixed tree $T$, we describe $\\mathrm{SPEX}(n,T)$ and consequently, bound $\\mathrm{spex}(n,T)$ in terms of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.14908","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/2505.14908/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"}