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Yu. M. Lifshits

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.

Discrete Mathematics and Applications, Walter de Gruyter

Print ISSN: 0924-9266
Volume: 15, 05/2005
Pages: 365 - 375

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