Hind, H. R.; Oellermann, O. Menger-type results for three or more vertices. (English) Zbl 0974.05047 Congr. Numerantium 113, 179-204 (1996). Summary: Let \(G\) be a graph and let \(S\) be an independent set of \(n\) vertices of \(G\) with the property that removing fewer than \(k\) vertices in \(V(G) \setminus S\) from \(G\) leaves all vertices of \(S\) in the same component of \(G\). It is shown that for \(n=3\), 4 and \(k\geq 2\) the graph \(G\) contains \(\lfloor {1\over n-1} \lceil {nk\over 2} \rceil \rfloor\) connected subgraphs each of which contains all the vertices in \(S\), but which are otherwise vertex-disjoint. Furthermore this value is shown to be best possible. The case when \(n=2\) is Menger’s theorem. Cited in 1 ReviewCited in 10 Documents MSC: 05C40 Connectivity 05C35 Extremal problems in graph theory Keywords:connectivity; independent set; Menger’s theorem PDFBibTeX XMLCite \textit{H. R. Hind} and \textit{O. Oellermann}, Congr. Numerantium 113, 179--204 (1996; Zbl 0974.05047)