{"paper":{"title":"On the Bandwidth of the Kneser Graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Derrek Yager, Tao Jiang, Zevi Miller","submitted_at":"2015-12-22T02:58:24Z","abstract_excerpt":"Let $G = (V,E)$ be a graph on $n$ vertices and $f: V\\rightarrow [1,n]$ a one to one map of $V$ onto the integers $1$ through $n$. Let $dilation(f) =$ max$\\{ |f(v) - f(w)|: vw\\in E \\}$. Define the {\\it bandwidth} $B(G)$ of $G$ to be the minimum possible value of $dilation(f)$ over all such one to one maps $f$. Next define the {\\it Kneser Graph} $K(n,r)$ to be the graph with vertex set $\\binom{[n]}{r}$, the collection of $r$-subsets of an $n$ element set, and edge set $E = \\{ vw: v,w\\in \\binom{[n]}{r}, v\\cap w = \\emptyset \\}$. For fixed $r\\geq 4$ and $n\\rightarrow \\infty$ we show that $$B(K(n,r)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.06937","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"}