{"paper":{"title":"On the SIG dimension of trees under $L_{\\infty}$ metric","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.DS"],"primary_cat":"math.CO","authors_text":"L. Sunil Chandran, Rajesh Chitnis, Ramanjit Kumar","submitted_at":"2009-10-28T13:55:42Z","abstract_excerpt":"We study the $SIG$ dimension of trees under $L_{\\infty}$ metric and answer an open problem posed by Michael and Quint (Discrete Applied Mathematics: 127, pages 447-460, 2003). Let $T$ be a tree with atleast two vertices. For each $v\\in V(T)$, let leaf-degree$(v)$ denote the number of neighbours of $v$ that are leaves. We define the maximum leaf-degree as $\\alpha(T) = \\max_{x \\in V(T)}$ leaf-degree$(x)$. Let $S = \\{v\\in V(T) |$ leaf-degree$(v) = \\alpha\\}$. If $|S| = 1$, we define $\\beta(T) = \\alpha(T) - 1$. Otherwise define $\\beta(T) = \\alpha(T)$. We show that for a tree $T$, $SIG_\\infty(T) = \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.5380","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"}