Subdivisions of K5 in graphs embedded on surfaces with face-width at least 5

Roi Krakovski; D. Christopher Stephens; Xiaoya Zha

doi:10.1002/jgt.21700

Subdivisions of K₅ in graphs embedded on surfaces with face-width at least 5

Roi Krakovski, D. Christopher Stephens, Xiaoya Zha

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We prove that if G is a 5-connected graph embedded on a surface Σ (other than the sphere) with face-width at least 5, then G contains a subdivision of K₅. This is a special case of a conjecture of P. Seymour, that every 5-connected nonplanar graph contains a subdivision of K ₅. Moreover, we prove that if G is 6-connected and embedded with face-width at least 5, then for every v â̂̂ V(G), G contains a subdivision of K₅ whose branch vertices are v and four neighbors of v.

Original language	English
Pages (from-to)	182-197
Number of pages	16
Journal	Journal of Graph Theory
Volume	74
Issue number	2
DOIs	https://doi.org/10.1002/jgt.21700
State	Published - 1 Jan 2013

Keywords

5-connected
K-5
face-width 5
representativity 5
subdivisions

ASJC Scopus subject areas

Geometry and Topology

Access to Document

10.1002/jgt.21700

Cite this

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title = "Subdivisions of K5 in graphs embedded on surfaces with face-width at least 5",

abstract = "We prove that if G is a 5-connected graph embedded on a surface Σ (other than the sphere) with face-width at least 5, then G contains a subdivision of K5. This is a special case of a conjecture of P. Seymour, that every 5-connected nonplanar graph contains a subdivision of K 5. Moreover, we prove that if G is 6-connected and embedded with face-width at least 5, then for every v {\^a}{\^̂} V(G), G contains a subdivision of K5 whose branch vertices are v and four neighbors of v.",

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T1 - Subdivisions of K5 in graphs embedded on surfaces with face-width at least 5

AU - Krakovski, Roi

AU - Stephens, D. Christopher

AU - Zha, Xiaoya

PY - 2013/1/1

Y1 - 2013/1/1

N2 - We prove that if G is a 5-connected graph embedded on a surface Σ (other than the sphere) with face-width at least 5, then G contains a subdivision of K5. This is a special case of a conjecture of P. Seymour, that every 5-connected nonplanar graph contains a subdivision of K 5. Moreover, we prove that if G is 6-connected and embedded with face-width at least 5, then for every v â̂̂ V(G), G contains a subdivision of K5 whose branch vertices are v and four neighbors of v.

AB - We prove that if G is a 5-connected graph embedded on a surface Σ (other than the sphere) with face-width at least 5, then G contains a subdivision of K5. This is a special case of a conjecture of P. Seymour, that every 5-connected nonplanar graph contains a subdivision of K 5. Moreover, we prove that if G is 6-connected and embedded with face-width at least 5, then for every v â̂̂ V(G), G contains a subdivision of K5 whose branch vertices are v and four neighbors of v.

KW - 5-connected

KW - K-5

KW - face-width 5

KW - representativity 5

KW - subdivisions

UR - https://www.scopus.com/pages/publications/84881480772

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DO - 10.1002/jgt.21700

M3 - Article

AN - SCOPUS:84881480772

SN - 0364-9024

VL - 74

SP - 182

EP - 197

JO - Journal of Graph Theory

JF - Journal of Graph Theory

IS - 2

ER -