Oellermann, Ortrud R. Major n-connected graphs. (English) Zbl 0687.05027 J. Aust. Math. Soc., Ser. A 47, No. 1, 43-52 (1989). The paper introduces major n-connected subgraphs with the following definitions: A major n-connected subgraph H of G is an induced subgraph of G with maximum order subject to having connectivity n and no proper subgraphs with connectivity exceeding n. A major subgraph is a subgraph of G which is major n-connected for some n. The major connectivity set, K(G) is defined to be the set of values n for which G has a major n- connected subgraph of order m, where m is the maximum order of a major subgraph. All of these definitions have edge analogues. For any set S of non negative integers, it is shown that there is some G for which \(S=K(G)\) and for \(m>\max \{s\in K(G)\},\) \(k\in K(G)\), every major k- connected subgraph of G has order m. Upper and lower bounds on the orders of such graphs are obtained. Reviewer: R.E.L.Aldred MSC: 05C40 Connectivity Keywords:subgraph connectivity; major n-connected subgraph; major subgraph; major connectivity set PDFBibTeX XMLCite \textit{O. R. Oellermann}, J. Aust. Math. Soc., Ser. A 47, No. 1, 43--52 (1989; Zbl 0687.05027)