{"paper":{"title":"Sharp results for the Erd\\H{o}s, Pach, Pollack and Tuza problem","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jorik Jooken, Stijn Cambie","submitted_at":"2025-02-12T18:27:15Z","abstract_excerpt":"We consider the Erd\\H{o}s, Pach, Pollack and Tuza problem, asking for the maximum diameter of a graph with given order $n$, minimum degree $\\delta$ and clique number at most $\\omega$. We solve their problem asymptotically for the first hard case, $\\omega \\leq 3$, for the smallest values of $\\delta$ by determining the smallest rational number $f(\\delta)$ such that $diam(G) \\leq f(\\delta)n+O(1)$ for all graphs $G$ with order $n$, minimum degree $\\delta$ and clique number $\\omega \\leq 3$. We also consider the weaker version where the clique number $\\omega \\leq 3$ is replaced by having chromatic n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.08626","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/2502.08626/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"}