Partitioning a $k$-connected graph

We study partitions of graphs by a system of disconnecting sets. We find a sharp upper bound for the number of resulting parts and analyse the case where the bound is attained. The result due to D. V. Karpov about the number of parts in a partition is proved under weaker constraints imposed on the graph. We also prove a theorem on bounding parts which yields an upper bound for the number of parts of the partition adjacent to a given vertex.
This research was supported by the Program of Fundamental Research of Presidium of the Russian Academy of Sciences ‘Research in base fields of modern mathematics’ and by the Program of the President of the Russian Federation for supporting the leading scientific schools, grant 2203.2003.1.