{"paper":{"title":"On the maximum diameter of $k$-colorable graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"\\'Eva Czabarka, Inne Singgih, L\\'aszl\\'o A. Sz\\'ekely","submitted_at":"2020-09-05T22:48:01Z","abstract_excerpt":"Erd\\H{o}s, Pach, Pollack and Tuza [J. Combin. Theory, B 47, (1989), 279-285] conjectured that the diameter of a $K_{2r}$-free connected graph of order $n$ and minimum degree $\\delta\\geq 2$ is at most $\\frac{2(r-1)(3r+2)}{(2r^2-1)}\\cdot \\frac{n}{\\delta} + O(1)$ for every $r\\ge 2$, if $\\delta$ is a multiple of $(r-1)(3r+2)$. For every $r>1$ and $\\delta\\ge 2(r-1)$, we create $K_{2r}$-free graphs with minimum degree $\\delta$ and diameter $\\frac{(6r-5)n}{(2r-1)\\delta+2r-3}+O(1)$, which are counterexamples to the conjecture for every $r>1$ and $\\delta>2(r-1)(3r+2)(2r-3)$. The rest of the paper prove"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.02611","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/2009.02611/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"}