Subdivisions of  K  5  in Graphs Embedded on Surfaces With Face‐Width at Least 5 | Zendy

Krakovski Roi | Zendy; Stephens D. Christopher | Zendy; Zha Xiaoya | Zendy

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Subdivisions of K 5 in Graphs Embedded on Surfaces With Face‐Width at Least 5

Author(s) -

Krakovski Roi,

Stephens D. Christopher,

Zha Xiaoya

Publication year - 2013

Publication title -

journal of graph theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.164

H-Index - 54

eISSN - 1097-0118

pISSN - 0364-9024

DOI - 10.1002/jgt.21700

Subject(s) - subdivision , combinatorics , conjecture , mathematics , graph , face (sociological concept) , surface (topology) , discrete mathematics , geometry , geography , social science , archaeology , sociology

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 K 5 . 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 ∈ V (G), G contains a subdivision of K 5 whose branch vertices are v and four neighbors of v .

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