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On Edge Cut of Graphs Leaving Components of Order at Least Five

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Abstract

An edge cut of a connected graph is 5-restricted if its removal leaves every component having order at least five. Graphs that contain 5-restricted edge cuts are characterized in this paper. As a result, it is shown that a connected graph G of order at least 13 contains 5-restricted edge cuts if and only if \({G \setminus v}\) contains a component of order at least five for every vertex v of graph G.

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Authors and Affiliations

  1. School of Mathematics, Shandong University, Jinan, 250100, China

    Jichang Wu

  2. Department of Mathematics, Wuyi University, Jiangmen, 529020, China

    Jianping Ou

Authors
  1. Jichang Wu
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  2. Jianping Ou
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Correspondence to Jichang Wu.

Additional information

Supported by National Natural Science Foundation Youth Found of China (10801091; 11126326).

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Wu, J., Ou, J. On Edge Cut of Graphs Leaving Components of Order at Least Five. Graphs and Combinatorics 29, 1973–1981 (2013). https://doi.org/10.1007/s00373-012-1182-y

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  • DOI: https://doi.org/10.1007/s00373-012-1182-y

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