Abstract
An m-restricted edge cut is an edge cut that separates a connected graph into a disconnected one with no components having order less than m. m-restricted edge connectivity λ m is the cardinality of a minimum m-restricted edge cut. Let G be a connected k-regular graph of order at least 2m that contains m-restricted edge cuts and X be a subgraph of G. Let ∂(X) denote the number of edges with one end in X and the other not in X and ξ m = min{∂(X) : X is a connected vertex-induced subgraph of order m}. It is proved in this paper that if G has girth at least m/2+ 2, then λ m ≤ ξ m . The upper bound of λ m is sharp.
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Supported by National Natural Science Foundation of China (Grant No.10271105) and Doctoral Fund of Zhangzhou Normal College.
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Ou, Jp., Zhang, Fj. Bound on m-restricted Edge Connectivity. Acta Mathematicae Applicatae Sinica, English Series, English Series 19, 505–510 (2003). https://doi.org/10.1007/s10255-003-0127-x
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DOI: https://doi.org/10.1007/s10255-003-0127-x