{"paper":{"title":"On a problem by Shapozenko on Johnson graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Llu\\'is Vena, Oriol Serra, V\\'ictor Diego","submitted_at":"2016-04-18T11:05:53Z","abstract_excerpt":"The Johnson graph $J(n,m)$ has the $m$--subsets of $\\{1,2,\\ldots,n\\}$ as vertices and two subsets are adjacent in the graph if they share $m-1$ elements. Shapozenko asked about the isoperimetric function $\\mu_{n,m}(k)$ of Johnson graphs, that is, the cardinality of the smallest boundary of sets with $k$ vertices in $J(n,m)$ for each $1\\le k\\le {n\\choose m}$. We give an upper bound for $\\mu_{n,m}(k)$ and show that, for each given $k$ such that the solution to the Shadow Minimization Problem in the Boolean lattice is unique, and each sufficiently large $n$, the given upper bound is tight. We als"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.05084","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":""},"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"}