### Resumen

It is well known that in finite graphs, large complete minors/topological minors can be forced by assuming a large average degree. Our aim is to extend this fact to infinite graphs. For this, we generalize the notion of the relative end degree, which had been previously introduced by the first author for locally finite graphs, and show that large minimum relative degree at the ends and large minimum degree at the vertices imply the existence of large complete (topological) minors in infinite graphs with countably many ends.

Idioma original | English |
---|---|

Páginas (desde-hasta) | 697-707 |

Número de páginas | 11 |

Publicación | SIAM Journal on Discrete Mathematics |

Volumen | 27 |

N.º | 2 |

DOI | |

Estado | Published - 2013 |

### Huella dactilar

### ASJC Scopus subject areas

- Mathematics(all)

### Citar esto

*SIAM Journal on Discrete Mathematics*,

*27*(2), 697-707. https://doi.org/10.1137/100819722

}

*SIAM Journal on Discrete Mathematics*, vol. 27, n.º 2, pp. 697-707. https://doi.org/10.1137/100819722

**Forcing large complete (topological) minors in infinite graphs.** / Stein, Maya; Zamora, José.

Resultado de la investigación: Article

TY - JOUR

T1 - Forcing large complete (topological) minors in infinite graphs

AU - Stein, Maya

AU - Zamora, José

PY - 2013

Y1 - 2013

N2 - It is well known that in finite graphs, large complete minors/topological minors can be forced by assuming a large average degree. Our aim is to extend this fact to infinite graphs. For this, we generalize the notion of the relative end degree, which had been previously introduced by the first author for locally finite graphs, and show that large minimum relative degree at the ends and large minimum degree at the vertices imply the existence of large complete (topological) minors in infinite graphs with countably many ends.

AB - It is well known that in finite graphs, large complete minors/topological minors can be forced by assuming a large average degree. Our aim is to extend this fact to infinite graphs. For this, we generalize the notion of the relative end degree, which had been previously introduced by the first author for locally finite graphs, and show that large minimum relative degree at the ends and large minimum degree at the vertices imply the existence of large complete (topological) minors in infinite graphs with countably many ends.

KW - Degree

KW - Infinite graph

KW - Minor

KW - Topological minor

UR - http://www.scopus.com/inward/record.url?scp=84880400194&partnerID=8YFLogxK

U2 - 10.1137/100819722

DO - 10.1137/100819722

M3 - Article

AN - SCOPUS:84880400194

VL - 27

SP - 697

EP - 707

JO - SIAM Journal on Discrete Mathematics

JF - SIAM Journal on Discrete Mathematics

SN - 0895-4801

IS - 2

ER -