### Abstract

An m-covering of a graph G is a spanning subgraph of G with maximum degree at most m. In this paper, we shall show that every 3-connected graph on a surface with Euler genus k ≥ 2 with sufficiently large representativity has a 2-connected 7-covering with at most 6k - 12 vertices of degree 7. We also construct, for every surface F^{2} with Euler genus k ≥ 2, a 3-connected graph G on F^{2} with arbitrarily large representativity each of whose 2-connected 7-coverings contains at least 6k - 12 vertices of degree 7.

Original language | English |
---|---|

Pages (from-to) | 26-36 |

Number of pages | 11 |

Journal | Journal of Graph Theory |

Volume | 43 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2003 May |

### ASJC Scopus subject areas

- Geometry and Topology

## Fingerprint Dive into the research topics of '2-connected 7-coverings of 3-connected graphs on surfaces'. Together they form a unique fingerprint.

## Cite this

Kawarabayashi, K. I., Nakamoto, A., & Ota, K. (2003). 2-connected 7-coverings of 3-connected graphs on surfaces.

*Journal of Graph Theory*,*43*(1), 26-36. https://doi.org/10.1002/jgt.10101