{"paper":{"title":"On the ratio of maximum and minimum degree in maximal intersecting families","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bal\\'azs Patk\\'os, Lale \\\"Ozkahya, M\\'at\\'e Vizer, Zolt\\'an Lor\\'ant Nagy","submitted_at":"2011-09-06T06:24:44Z","abstract_excerpt":"To study how balanced or unbalanced a maximal intersecting family $\\mathcal{F}\\subseteq \\binom{[n]}{r}$ is we consider the ratio $\\mathcal{R}(\\mathcal{F})=\\frac{\\Delta(\\mathcal{F})}{\\delta(\\mathcal{F})}$ of its maximum and minimum degree. We determine the order of magnitude of the function $m(n,r)$, the minimum possible value of $\\mathcal{R}(\\mathcal{F})$, and establish some lower and upper bounds on the function $M(n,r)$, the maximum possible value of $\\mathcal{R}(\\mathcal{F})$. To obtain constructions that show the bounds on $m(n,r)$ we use a theorem of Blokhuis on the minimum size of a non-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.1079","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":""},"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"}