### 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 |
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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 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Journal of Graph Theory*,

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

**2-connected 7-coverings of 3-connected graphs on surfaces.** / Kawarabayashi, Ken Ichi; Nakamoto, Atsuhiro; Ota, Katsuhiro.

Research output: Contribution to journal › Article

*Journal of Graph Theory*, vol. 43, no. 1, pp. 26-36. https://doi.org/10.1002/jgt.10101

}

TY - JOUR

T1 - 2-connected 7-coverings of 3-connected graphs on surfaces

AU - Kawarabayashi, Ken Ichi

AU - Nakamoto, Atsuhiro

AU - Ota, Katsuhiro

PY - 2003/5

Y1 - 2003/5

N2 - 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 F2 with Euler genus k ≥ 2, a 3-connected graph G on F2 with arbitrarily large representativity each of whose 2-connected 7-coverings contains at least 6k - 12 vertices of degree 7.

AB - 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 F2 with Euler genus k ≥ 2, a 3-connected graph G on F2 with arbitrarily large representativity each of whose 2-connected 7-coverings contains at least 6k - 12 vertices of degree 7.

UR - http://www.scopus.com/inward/record.url?scp=0037950132&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0037950132&partnerID=8YFLogxK

U2 - 10.1002/jgt.10101

DO - 10.1002/jgt.10101

M3 - Article

VL - 43

SP - 26

EP - 36

JO - Journal of Graph Theory

JF - Journal of Graph Theory

SN - 0364-9024

IS - 1

ER -