On the existence of edge cuts leaving several large components

Rautenbach, Dieter GND; Volkmann, Lutz GND

We characterize graphs of large enough order or large enough minimum degree which contain edge cuts whose deletion results in a graph with a specified number of large components. This generalizes and extends recent results due to Ou (Edge cuts leaving components of order at least m, Discrete Math. 305 (2005), 365-371) and Zhang and Yuan (A proof of an inequality concerning k-restricted edge connectivity, Discrete Math. 304 (2005), 128-134).


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