{"paper":{"title":"Note on the minimal size of a graph with generalized connectivity kappa_3= 2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Shasha Li, Xueliang Li, Yongtang Shi","submitted_at":"2011-06-22T10:34:25Z","abstract_excerpt":"The concept of generalized $k$-connectivity $\\kappa_{k}(G)$ of a graph $G$ was introduced by Chartrand et al. in recent years. In our early paper, extremal theory for this graph parameter was started. We determined the minimal number of edges of a graph of order $n$ with $\\kappa_{3}= 2$, i.e., for a graph $G$ of order $n$ and size $e(G)$ with $\\kappa_{3}(G)= 2$, we proved that $e(G)\\geq (6/5)n$, and the lower bound is sharp by constructing a class of graphs, only for $n\\equiv 0 \\ (mod \\ 5)$ and $n\\neq 10$. In this paper, we improve the lower bound to $\\lceil(6/5)n\\rceil$. Moreover, we show tha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.4411","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"}