# On the Decomposition of a 3-Connected Graph into Cyclically 4-Edge-Connected Components

## Abstract

A graph is called cyclically 4-edge-connected if removing any three edges from it results in a graph in which at most one connected component contains a cycle. A 3-connected graph is 4-edge-connected if and only if removing any three edges from it results in either a connected graph or a graph with exactly two connected components one of which is a single-vertex one. We show how to associate with any 3-connected graph a tree of components such that every component is a 3-connected and cyclically 4-edge-connected graph.

- Authors:

- St.Petersburg Department of Steklov Institute of Mathematics and Peter the Great St.Petersburg Polytechnic University (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22774015

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Mathematical Sciences

- Additional Journal Information:
- Journal Volume: 232; Journal Issue: 1; Other Information: Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1072-3374

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; DECOMPOSITION; GRAPH THEORY; MATHEMATICAL SOLUTIONS

### Citation Formats

```
Pastor, A. V., E-mail: pastor@pdmi.ras.ru.
```*On the Decomposition of a 3-Connected Graph into Cyclically 4-Edge-Connected Components*. United States: N. p., 2018.
Web. doi:10.1007/S10958-018-3859-0.

```
Pastor, A. V., E-mail: pastor@pdmi.ras.ru.
```*On the Decomposition of a 3-Connected Graph into Cyclically 4-Edge-Connected Components*. United States. doi:10.1007/S10958-018-3859-0.

```
Pastor, A. V., E-mail: pastor@pdmi.ras.ru. Sun .
"On the Decomposition of a 3-Connected Graph into Cyclically 4-Edge-Connected Components". United States. doi:10.1007/S10958-018-3859-0.
```

```
@article{osti_22774015,
```

title = {On the Decomposition of a 3-Connected Graph into Cyclically 4-Edge-Connected Components},

author = {Pastor, A. V., E-mail: pastor@pdmi.ras.ru},

abstractNote = {A graph is called cyclically 4-edge-connected if removing any three edges from it results in a graph in which at most one connected component contains a cycle. A 3-connected graph is 4-edge-connected if and only if removing any three edges from it results in either a connected graph or a graph with exactly two connected components one of which is a single-vertex one. We show how to associate with any 3-connected graph a tree of components such that every component is a 3-connected and cyclically 4-edge-connected graph.},

doi = {10.1007/S10958-018-3859-0},

journal = {Journal of Mathematical Sciences},

issn = {1072-3374},

number = 1,

volume = 232,

place = {United States},

year = {2018},

month = {7}

}

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