## Abstract

Let G be a 4-connected graph. We call an edge e of G removable if the following sequence of operations results in a 4-connected graph: Delete e from G; if there are vertices with degree 3 in G-e, then for each (of the at most two) such vertex x, delete x from G-e and turn the three neighbors of x into a clique by adding any missing edges (avoiding multiple edges). In this paper, we continue the study on the distribution of removable edges in a 4-connected graph G, in particular outside a cycle of G or in a spanning tree or on a Hamilton cycle of G. We give examples to show that our results are in some sense best possible.

Original language | English |
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Pages (from-to) | 559-587 |

Number of pages | 29 |

Journal | Discussiones Mathematicae - Graph Theory |

Volume | 41 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1 May 2021 |

## Keywords

- 4-connected graph
- atom
- fragment
- removable edge