Abstract
A graphG is called a block—cactus graph if each block ofG is complete or a cycle. In this paper, we shall show that a block—cactus graphG has the property that the cardinality of a smallest set separating any vertex setJ ofG is the maximum number of internally disjoint paths between the vertices ofJ if and only if every block ofG contains at most two cut-vertices. This result extends two theorems of Sampathkumar [4] and [5].
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Guo, Y., Volkmann, L. A generalization of menger's theorem for certain block—cactus graphs. Graphs and Combinatorics 11, 49–52 (1995). https://doi.org/10.1007/BF01787420
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DOI: https://doi.org/10.1007/BF01787420