Schmidt, Jens M.Jens M.Schmidt2020-10-192020-10-192018-05Journal of Graph Theory (2018)http://hdl.handle.net/11420/7609For minimally k-connected graphs on n vertices, Mader proved a tight lower bound for the number |Vk| of vertices of degree k in dependence on n and k. Oxley observed 1981 that in many cases a considerably better bound can be given if m : |E| is used as additional parameter, i.e. in dependence on m, n, and k. It was left open to determine whether Oxley's more general bound is best possible. We show that this is not the case, but give a closely related bound that deviates from a variant of Oxley's long-standing one only for small values of m. We prove that this new bound is best possible. The bound contains Mader's bound as special case.en0364-9024Journal of graph theory20181146153lower boundsminimally k-connected graphstightvertices of degree kMathematikTight bounds for the vertices of degree k in minimally k-connected graphsJournal Article10.1002/jgt.22202Other