Forcing large complete (topological) minors in infinite graphs

Maya Stein, José Zamora

Resultado de la investigación: Article

2 Citas (Scopus)

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 originalEnglish
Páginas (desde-hasta)697-707
Número de páginas11
PublicaciónSIAM Journal on Discrete Mathematics
Volumen27
N.º2
DOI
EstadoPublished - 2013

Huella dactilar

Infinite Graphs
Forcing
Minor
Finite Graph
Minimum Degree
Imply
Generalise

ASJC Scopus subject areas

  • Mathematics(all)

Citar esto

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

En: SIAM Journal on Discrete Mathematics, Vol. 27, N.º 2, 2013, p. 697-707.

Resultado de la investigación: Article

TY - JOUR

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AU - Zamora, José

PY - 2013

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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.

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KW - Degree

KW - Infinite graph

KW - Minor

KW - Topological minor

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JF - SIAM Journal on Discrete Mathematics

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